Evol. Inst. Econ. Rev. 4(1): 143–170 (2007)

ARTICLE

Econo-physics: A Perspective of Matching Two Sciences
Yuri YEGOROV
Institute for Advanced Studies, Stumpergasse 56, A-1060, Vienna, Austria, and University of Vienna, Department of Industry and Energy, Brünner Strasse, 72, A-1210, Vienna, Austria. E-mail: yegorov@ihs.ac.at Abstract The present article marks some potentially fruitful dimensions of economic research based on principles of economic theory but using more analogies with physics. Molecular structure of society with its different states, principles generating spontaneous order different from “invisible hand”, social analogies of the concepts of temperature and pressure in physics are investigated. Some analogies between phase transitions in physics and transition between different social regimes can reveal the areas of stability of liberal regimes as well as possibility of spontaneous emergence of different social orders. A possibility to expand neoclassical economics to capture Marxism and nationalism in a formal mathematical framework is also discussed. Keywords: economic structures, origin of order, econo-physics, socio-physics.

1.

Introduction

This article is methodological. It focuses on economic and social questions that are rarely touched by economic theorists despite their obvious importance for our understanding of economic processes in the world. No fully formalized model will be proposed here. Instead, the focus will be on interaction between economic elements and emergence of structures. These ideas have been successfully elaborated in natural science by physicists. That is why it makes sense to look for some analogies between physical and economic concepts, and then to find ways of employing principles of modelling from physcis into economic science. The term “econophysics” is already used in narrow sense, to describe models of financial markets using some ideas from physics (see Mantegna and Stanley, 2000). However, the cross-fertilization between these two sciences allows for a wider treatment. That is why here we will use another word “econo-physics” (and sometimes “sociophysics”), following the paper by Aruka and Mimkes (2006) in order to escape
JEL: B41, B51, B52, F02, P25.

Y. YEGOROV

misunderstanding in terminology. While the word “socio-physics” was not commonly accepted among scientists that work in this field, there exist fundamental contribution to this field from such authors as Haken (1977) and Weidlich (2002). 1.1 Motivation The main goal of this paper is to describe directions of fruitful explorations, based on past positive experience of physics and taking into account specific economic assumptions. There is no criticism here about microeconomic preferences, but more about little explored directions in economic science. The other goals of this article are: a) b) c) d) to put some of the ideas into a language more common for economists (thus, not to escape utility function, etc); to describe different social organizations and ideologies of society (nationalism, Marxism) in a mathematical framework that naturally extends classical economics; to discuss multiplicity of social order-generating principles; to discuss phases and phase transition in society. Physics is a science about structures, their emergence and transformation. All the nature has different level of organizations, and macro properties can be derived on the basis of micro elements and interactions between them. Economics seems to move a similar path, since agents are considered as fundamental elements, like atoms in physics. However, economics at present is linear science in a sense that it puts an individual at the absolute level and does not consider endogeneous emergence of structures of individuals. Clearly, the primitives may be not individual agents but firms (in industrial organization) or countries (in macroeconomics). However, little is done to understand what kind of interactions bring individuals to the further level of organization (firms, countries, etc). Physics has great experience of building links between micro and macro levels. Statistical physics is the branch of physics that derives the changes of macro states of matter through micro parameters. The theory of waves in continuous media focuses on the link between micro and macro levels but in different research field. There the local interaction between small subsets (neighbourhoods) leads to emergence of complex dynamics in space and time. Physical chemistry studies the transformation of properties of matter when coupling occurs at the level of (elementary) atoms that can form different types of molecules. Finally, nuclear physics is about transformations inside atoms changing their structure. Clearly, not all of these transitions from micro to different macro levels can be successfully implemented in economics. For example, changing internal structure of atom would mean, if we employ the analogy between atom and economic agent, the
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Econo-physics: A Perspective of Matching Two Sciences

change of agent’s nature. It may be of biological or psychological origin, but typically economics consider individuals as stable over time. This change, for example evolution of preferences with ageing, can be an interesting economic question, but it will not be elaborated here. There also exist some problems with application of mathematically rich theory of waves to economics. The problem is that there are too few observations confirming existence of economic processes with deterministic cyclical origin. But while economics is unlikely to give very rich field for mathematical models of regular wave structures with deterministic nature, there still exist some works in this direction. That is why analogies with statistical mechanics and physical chemistry might find easier application in economic models. And this paper will concentrate more on these issues. Section 2 is oriented on the necessity of common language of economics and physics in order to deal with the phenomena of molecular structure of society. Section 3 is devoted to origins of social order, that are complementary to market forces. Section 4 introduces thermodynamic concepts for society (analogies of temperature and pressure) and describes several social types (solid, liquid and gas) that depend on combination of these parameters. The role of altruism in preferences is discussed in Section 5. This goes in line with new concepts elaborated in the book of Bowles (2003). Moreover, adding altruism into preferences allows to describe not only liberal society (like neoclassical economics does) but also societies of Marxist and nationalist types. Altruistic preferences bring more solid grounding to emergence of social structures. Existing types of equilibria developed by non-cooperative game theory are rather weak and unstable, while even small altruistic element can make them more robust. An example is provided. Section 6 deals with potential applications. 1.2 Link with modern paradigms in sciences The agenda presented in abstract is unusual for a paper in economic theory. An important aspect is related to heterogeneity and structure. While it is true that physicists also consider the world to be formed of a large number of elementary objects (atoms from the time from Aristotle to Newton, and elementary particles or quarks at later stage), these particles are interacting not equally with each other, since this interaction depends on distance and since they are located in different points in space at any time moment. Clusters of particles form different structures starting from molecules and ending with crystals. This gives self-evolving patterns, which at one level of abstraction can be described as wave motion and at the other level as phase transition. My agenda would be not in putting in doubt some mutually recognized principles of economic science but rather to focus the attention on its limitation in conceptual sense.
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That is why I want to keep all these assumptions about utility and rationality, but to consider also some other conditions (acting as external forces). Different sections would deal with some philosophical and methodological aspects of creating models in economics. 1.3 Related literature The ideas of unified science, including economics and physics, have been expressed more than a century ago. The 120-year old ideas of Serhij Podolinsky to combine Marxism with ecology have been rejected by Marxists. Proposal for unified science was expressed by Otto Neurath in 1920s.1) Economics should include physical aspects of human ecology, study of cultural, social, ethical influences on production and consumption (see Krishan et al. (1995)). This agenda became critically important in the last 3 decades of the 20th century, when ecologists realized the danger of combining the reality of exhaustible resources with the continuing growth of population and production. The necessity of ecological economics was formulated by Goodwin. He proves the existence of substantial set of questions, which are addressed to real economic problems and located on the frontier of traditional economic science, and tries to study questions on the intersection of different sciences. He says that “if the study of economics is to be of value to society it must stress the aspects of economic behaviour that matter the most”.2) A number of critical areas of economic thought have been left by mainstream economists on the margin. He argues that while the relevant agenda was formulated by classics of economics in the past, some priorities have been shifted later. For example, Adam Smith put similar value to the concepts of wealth, morality and nation, but currently the last two concepts are out of interest of mainstream economics. Similarly, von Thünen in 1826 pioneered the research of spatial economic structures, which later became a part of regional science, but this field is left out of major economic textbooks in microeconomics. Ecological economics, although inspired by ecological degradation and ideas of sustainable development, is not a science of ecology, but also addresses the questions of evolution of purely economic systems (see ch. 8 in Faber et al. (1996)). The authors use a parallel between physics, theoretical biology and economics and try to classify what processes are predictable and non-predictable in all these sciences. Physical systems exhibit the highest degree of predictability, due to lower complexity, partly in deterministic and partly in stochastic terms. This was the major reason of successful
1) 2)

See the summary of “The history of future” by J. Martinez-Alier and K. Schluppman there. See introduction to the book by Krishan et al. (1995)

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Econo-physics: A Perspective of Matching Two Sciences

development of mathematical tools describing dynamical systems in physics. Economics also exhibit phenomena, which are completely predictable, and establishing of market equilibria is one of such phenomena. However, economics does not use all available techniques from physics to explain other classes of processes that are also predictable. The difficulty of economic modelling can be easier understood on the basis of statement of theoretical biology about “fundamental unpredictability of genotypic evolution”, in contrast to phenotypic evolution. The economic analogy of genotype is innovation. While evolutionary path after innovation occurs can be predicted, the moment of innovation cannot. Here the issues of non-predictability and evolution will not be substantially elaborated. Instead, more attention will be paid to structures and mechanisms of their emergence and survival under changing conditions. This already represents wide direction of research, and little analytical work was done here by economists so far. A nice exception is the book of Bowles (2003), where he suggests evolutionary theory of institutions. Non-market social interactions represent one of key points of his research. He studies co-evolution of individual preferences and structures of markets using dynamic models. This agenda differs substantially from one delivered by classical microeconomics, but it allows to explain much more historical episodes and empirical puzzles. In the article by Aruka and Mimkes (2006) different areas of influence of physical ideas on social sciences and economics are discussed. The importance of considering heterogeneous interacting agents is stressed. While agents’ heterogeneity is sometimes present in economic models,3) most of classical economic papers deal with homogeneous individualistic agents. Such an approach is easier from methodological perspectives, because it allows to build self-consistent economic theory based on rationality principles, while heterogeneous assumption often requires the shift to bounded rationality. Following the principles of homogeneity and full rationality limits the possibility of modelling real social phenomena (like wealth distribution) and broadens the gap between theoretical and empirical economics. The role of synergetics (see Haken (1977)) in understanding social dynamics is important. There are two levels: micro and macro. Macrodynamic evolution is dominated by few key variables, named order-parameters. Macro states of a social system are described in probabilistic terms. The central equation of evolution for the probability distribution over the macro variables is called Master equation (see Weidlich
3)

In fact, WEHIA conferences by definition deal with this type of agents.

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(2002, 2006)). The main claim of the work by Bowles and Gintis (2005) is that “other-regarding preferences such as altruism and reciprocity are essential” for understanding why humans are cooperative. At the first glance, cooperation often takes place even if the preferences are self-regarding (like in almost all research of economics). However, these theories are not sufficient to explain all evidence. For example, reciprocal altruism provide some explanation of cooperation among dyads, but not in larger groups and when future interactions are unlikely. Kara-Murza (2002) writes that Thomas Gobbs has developed the myth about man as egoistic and individualistic atom. These “atomic” ideas emerge every time when ruling groups want to impose liberal economics in the society. Emergence of industry and market economy required the freedom of a man from conservative political, economical and cultural structures. The ideas of atomism and rationality allow solving two ideological tasks of rising bourgeoisie: to legitimate new political order and new economic order. Skirbekk (2003) analyses the negative influence of the presently dominant liberal ideology on social moral, growing instability of family and argue about the missed positive elements of traditional cultures and ideologies that went to decline in the end of the 20th century. Emergence of structures (large groups, countries) resembles emergence of molecules or crystals from atoms. In physics, this requires the field of interaction. The standard assumptions of economic theory (self-regarding preferences, non-convexities) do not allow for emergence of such structures. Thus they are either considered as given (firm, state) or not considered at all. The papers of Yegorov (2001b, 2005a) study the emergence of such groups on the assumption of non-convex technology that makes it optimal for group members to keep group growing in a dynamic sense until it reaches its optimal size. Also, the conditions of country emergence are considered. It is shown that a territory of certain size becomes an optimal structure for its inhabitants (assumed to be homogeneous) when we move from micro to macro level and consider the balance between benefits from harvesting certain territory and the costs to protect its border and to maintain centralized structure that needs communication with all points (regions) for efficient management. As will be claimed later, both spatial structures in economics (location heterogeneity plus transport cost) and scale economies play important roles as origins of order in society. Some ideas of the author in both of these areas can be taken from Yegorov
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Econo-physics: A Perspective of Matching Two Sciences

(1998, 2001ab, 2005ab). 2. Working Out Common Language between Economics and Physics

The tragedy of contemporary science is an increased specialization, leading to impossibility of general public to understand science. This property was mentioned by Kuhn (1970). That is why one cannot use the language of most sophisticated concepts inside physics and economics. In order to be understandable to more scientists, it is better to use relatively simple concepts from both sciences and to find link across them. Only simple concepts from physics such as “particles”, “state of matter”, “field”, “energy”, which are studied in school, will be employed here. Economic concepts of similar simplicity would be employed as analogy. I am fully aware that complete analogy is impossible, but even incomplete analogy can be powerful. Below I introduce several concepts that can be used as approximate translations from language of “physics” to “economics” and visa versa. Elements The elements in physics are “particles”, “atoms”, while in economics the analogy is played by “agents”. Clearly, there is a difference since particles cannot think, while agents obey laws of behaviour different from particles. But the analogy can be exploited when we are doing aggregation and consider nonlinear interactions between elements. Simple structures In physics “molecules” represent a relatively stable union of a small number of atoms. Similar structures also exist in economics; for example, family or small business. Complex structures In physics complex structures emerge on macro level. In statistical physics, the microstate is a set of many particles with their coordinates and velocities (which is never completely observed). The parameters of macro-state (temperature, pressure) can be measured. Physics knows how to interrelate macroparameters with distribution of microparameters. Economics is addressing similar models when it talks about aggregation, from micro to macro level.4) Economy, state or global society are examples of complex structures in economics. Interaction In physics, particles interact via the field. All fields are usually declining with distance according to a particular inverse power law. The coordinates of particles make them naturally asymmetric with respect to field. Depending on initial conditions, different
4)

See the papers of Hildenbrandt.

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structures can emerge. For example, gravity force has created a system of planets. On micro-level, molecules are stable structures of the field generated by particles. It is worthwhile mentioning that nonlinearity and heterogeneity are responsible for emergence of most structures. In economics, interaction is usually modelled as linear: agents contribute their endowments to the market, and take other products from there, according to their preferences. The only nonlinearity can come from utility, but as it is ordinal, this nonlinearity does not play a crucial role. Nevertheless, markets exhibit selforganizing property.5) Non-linear element of interaction among agents is given by externalities. The potential of externalities in building stable structures in economics is still under-exploited, and one of the goals of present work is to attract attention to this problem. Characteristics of elements In physics, particles are characterized by their coordinates, velocities and energies. Due to Heisenberg inequality from quantum mechanics, the first two parameters cannot be measured exactly on micro level. On the other hand, energy can be defined and measured. Economic science may also have a type of Heisenberg inequality, because some microeconomic parameters (like utility) are not observable directly. This is an interesting question, however it is not developed yet. In economics, an analogy of coordinates and velocities can be given by dynamic pattern of consumption bundle, while “wealth” (or income) is an analogy of energy. The latter can be easier observed. Thus, macroeconomic state should depend on wealth distribution of agents, which is measurable in reality. The role of wealth distribution for the stability of social structures will be discussed later. Characteristics of structures Structures in physics can be characterized by their total energy, mass, entropy, type of micro-order (crystal or gas, for example). In economics, macroeconomics deals with country’s GDP, interest rate, growth rate, etc. The parameters characterizing type of order (see section 3) are usually not studied by economics, although they represent an important macro characteristic of society. 2.1 Molecular structure of society Classical microeconomics and industrial organization consider the number of firms as given. Thus, they view firms like mechanics views atoms, but do not allow for an analogy of chemical reactions. In real business, firms may split, join together, be born and die.
5)

In the sense that they generate equilibrium under certain assumptions (see Arrow-Debreu theory).

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Econo-physics: A Perspective of Matching Two Sciences

Molecules of firms can form chains with local interaction. This is similar to a structure of polymer. The idea of “polymer society” is represented in the studies of network economics, especially the part related to emergence of random networks with short-scale or long scale links.6) Structures can be imposed (by state) or self-organized (emergence of small firms of Italian type, with about 10 workers, mostly relatives; or agricultural cooperatives). The influence of state on economy is studied by economics of public sector (see the book of Stiglitz (1988) as an example). Self-organization of structures can occur on the basis of mixed utility (see mathematical model subsequently). Physical analogy: forced order or crystallization in external field vs. spontaneously emerging clusters. Different particles of physical substance have different energy, and stable distribution of their velocities in gas can be an analogy to stable distribution of wealth in particular societies. This question of wealth distribution deserves special attention and will be briefly elaborated later. 3. Equilibrium, Structure and Order in Economics

The concept of equilibrium plays the major role in theoretical economics. The principle of equilibrium was brought to economics from mechanics. Equilibrium world was neither scientific nor logical conclusion. Equilibrium in economics was not a discovered law. Contrary, the search for economic laws was based on beliefs in equilibrium. All economics (political economy) starting from Adam Smith, neglects all sources of disequilibrium (see Kara-Murza (2002), pp. 124–125). 3.1 Why structure is important? When we look at structures in natural sciences (physics, chemistry, biology), we find that structure is some composition of elements which is relatively stable under some range of external parameters and thus can be observed. For example, some chemical elements are observed on earth in natural conditions, while other need some special laboratory conditions. Species and populations are biological structures, also composed of elements. When they die, they are decomposed back to sub-elements. In social sciences, structures include some composition of elementary agents: firms, clubs, countries, mankind. Neoclassical economics does not pay much attention to these structures. However, even its father, Adam Smith stressed the importance of states and nations as objects of study of economics. Neoclassical economics exploits another idea of Smith, “invisible hand”,
6)

See Stocker et al. (2000); there are also many unpublished drafts presented at conferences and seminars.

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which brings spontaneous order by market forces. Despite the relative success of this idea for explaining spontaneous order, it is clear that it is incomplete. 3.2 Structures and transition in Russia Application of ideas from neoclassical economics with welfare theorems to transition in Russia in 1992 was not a successful experiment. Only in 1999 J. Stiglitz has recognized that this type of transition was a mistake for Russia. Many structures have been destroyed during transition of 1990s. It was clear that changing environment should destroy some of the old order, but it is not clear how new order can emerge from chaos. Global shocks on Earth have led to death of some populations (dinosaurs). But they are not replaced immediately by new types of species. When a biological object dies, it dissolves into molecules, which give rise to emergence of some low-structured life (bacterias). It takes long time for evolution, for life of higher complexity to emerge. If the higher level of economy (high-tech industry) is dead during transition in a particular country (Russia), elements (capital and labour) become free. But capital in a form of constructions may become obsolete, while labour can find itself facing the only possibility to start individual activity or small business. It takes some time for high-level firms to organize on these ruins, and the only possibility is takeover by transnational companies. However, in 1990s capital was not flowing freely in Russia, and one reason behind that was described by Parshev (2001). I will not focus now more on transition. The goal was to show that study of emergence of structures is crucial and should be hot topic for modern economics which wants to explain processes in real but not imaginary world of abstract spaces that some part of modern economic theory does. 3.3 Origins of order in society It is important to formulate this philosophical question about origins of social order. While it is clear that its substantial investigation in one isolated article is impossible, it still makes sense to suggest some working hypothesis. There exists at least three main forces generating spontaneous order in economy. The first one is well known from microeconomic textbooks. It is linked with market forces caused by diminishing returns and competition (they are responsible for the effect of Adam Smith’s “invisible hand”). The second force comes from studies in regional science and economic geography (see, for example, Beckmann and Thisse (1986)). This force may bring complementary properties to those derived by non-spatial economic theory. For example, monopolistic competition of Chamberlin (1933) reveals the existence of spatial areas around a firm when they act as local monopolists and compete only through edge consumer.
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Econo-physics: A Perspective of Matching Two Sciences

Monopolistic competition with product differentiation (see, for example, Fujita, Krugman and Venables (1999)) rely on completely different case (methodological and topological), where consumers have access to all variety of commodities. Spatial forces based on transport cost and local interaction become responsible for geographical, location effect, which are always present and cannot be fully controlled by rational decisions. Some spatial effects are elaborated by Yegorov (2005b). The third self-organizing principle is based on nonlinear interaction of elements (when the whole is not exactly sum of its parts). Without trying to present sufficient literature survey on this topic, I will just mention two important publications: Arthur (1994) and Durlauf and Young (2001). This principle summarizes the self-organizing role of externalities. They can bring the difference between social outcome and individual preferences (like in segregation model of T. Schelling). They often lead to multiplicity of equilibria, also in dynamic sense. Role of space Space works as an element imposing heterogeneity (at least, with respect to distance), and thus bringing nonlinearity to interaction of a priori identical elements.7) But space also works as a stabilizing factor. For example, the IRS technology in a spaceless context gives rise to a firm of infinite size. With transport costs and topology of real geographical space, optimal cooperation extends to a particular spatial limit (see Yegorov (1998, 2001a)). Analogy with different sciences This duality between market and spatial forces is similar to one argument of social scientists about the role of biology and environment in human beings. Most likely, humans are not fully predetermined by genetics. Maugli’s example shows that an important part of individual formation depends on the environment. However, it would be too far-fetched to expect that everything depends on environment and has no relation to genetics and biology. Economists (except for regional scientists) mostly ignore the spatial forces. Another extreme view (complete geographic predetermination) is also unlikely to be true.

7)

Hence, agents equal in skills become unequal just due to location difference. This contrasts an approach of urban economics where at equilibrium such agents have a possibility to change location but are indifferent to do it. Frictions and historical factors might make this inequality persistent (like people got used to less productive land and not all migrate to the region where they would have higher productivity.)

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It makes sense to describe the mechanism of self-organization of spatial structures in economics. Geographical forces are considered as “gravity” by some economists, with complete copying of inverse power8) Newton’s law, and this has no microeconomic justification. But it is possible to build a simple model describing an emergence of a country of optimal size (Yegorov, 2005a) based on the principles of optimization, transport costs and Euclidean geometry applied to continuous space. Order-generating principles It makes sense to end this discussion with a potentially incomplete list of principles that generate order. 1. A common idea (religion, nation) can be responsible for non-market grouping of large number of people. Historically such groups had leaders accepted by all. This leads to society of crystal type, since agents sacrifice some part of individual preferences in favour of joint preferences of the society (nonlinearity). 2. Consider a community of farmers-landowners. When land slots are fixed by law (inheritance, etc), there no room for conflicts. Endogeneous cooperation can emerge in sharing machines, due to scale economies.9) Here we have mixed effect of spatial economics and nonlinearity. 3. The balance between increasing returns to scale and transport cost in the environment of consumers spread over space can lead to emergence of optimal spatial structures, which are vulnerable to the change of external parameters, like world price for energy or transport cost; see Yegorov (1998, 2005a). 4. Invisible hand is also responsible for emergence of order, and this is done by neoclassical microeconomics. However, some equilibria are not robust or dynamically unstable, and thus they are not considered in dynamic framework. 4. Role of Analogies of Temperature and Pressure in Society

Thermodynamics is one of branches of physics that is formally close to economic theory. Contrary to many “open branches” of physics that are not formalized axiomatically and develop together with new empirical findings, thermodynamics is deduced from a set of axioms and thus formally resembles the building of contemporary economic theory.
8) Newton’s law has inverse first power for potential, and inverse second for a force; economists more often use inverse first power. 9) This case was observed in 1920s in Soviet Union, after revolution and before collectivisation, which has not been endogeneous formation of cooperatives but too rapid process influenced by external force.

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However, there is an important difference in one property of studied processes. Thermodynamics studies irreversible processes. They are different from those in Newton mechanics, because at macro level (and thermodynamics formally deals with the properties of large groups of molecules, although a formal link between micro and macro levels is studied by statistical physics) time in physics becomes irreversible. For microeconomic theory this question is irrelevant, since it typically abstracts from dynamic processes. However, even if it would do dynamics (like macroeconomic growth models, for example), the principle of equilibrium would put important limits to the set of studied questions. In thermodynamics and statistical physics only a class of adiabatic processes (infinitely slow) is reversible. But the main goal of this section is different: it is related to finding the analogies between some macro variables in thermodynamics and in social science. 4.1 Analogies In physics, temperature T represents one of the parameters responsible for different states of matter as well as phase transitions between them.10) Temperature of gas is related to the average energy of molecules. The increase of temperature leads to the transition from solid state to liquid, and later to gas and plasma. The second parameter is pressure p. If temperature is kept constant, the decline of pressure works in a way similar to temperature increase. The thermodynamic state of gas in a fixed volume V is described by the law of BoyleMariott: pV Tc, where c is constant for fixed mass and chemical composition: c Rm/m . The average kinetic energy, K, of molecules in gas is much higher than potential energy of interaction, ∏: K/∏ relation is reversed: K/∏ 1. For liquid, they are of similar order, while for solid state the 1.

Low temperature and high pressure create crystals with long-scale order. High temperature and low pressure create gas with no order, practically chaotic motion. Liquid is an intermediate stage, while liquid polymer is a particular case of rather complex chain structure. Now consider social analogies. Temperature is an analogy of economic wealth w, while inverse pressure is an analogy of economic freedom, f.11) The increase of wealth and individual freedom should lead dictatorship to democracy through a chain of
In fact, this is a general philosophical law of transformation of quantitative change into qualitative change, discovered by Hegel. 11) While it is difficult to propose quantitative formula for economic freedom, it is clear that one is higher in democratic society than under dictatorship.
10)

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intermediate states. There is an analogy between dictatorship and solid state, and between democracy and gas. For dictatorship, the ratio of individual energy to social energy (measured for example, as the share of freely disposable income in per capita GDP) is low, while for democracy it is high. Another prediction based on physical analogy is that democracies should be richer societies than dictatorships. 4.2 Solid, liquid and gas-type societies In nature we have a variety of different chemical substances with a common property: to be sequentially in solid, liquid and gas states depending on temperature and pressure. The trip of “Voyager” towards giants of the Solar system has discovered different substances on different planets to be in states different from those on the Earth. This is a collective interaction of identical elements, that gives rise to different states under different external conditions. Although the similar theory of society is currently absent, economic models involve representative agents which to some extent are analogies of atoms or molecules.12) We observe societies (also in historical retrospect) with different level of individual freedom. In dictatorships we have low level of individual activity in comparison to social; these are “solid” societies. Fully liberal societies (where the role of state can be asymptotically neglected) have unrestricted individual activity, and all equilibria (at least in neoclassical economic models) emerge under this assumption. The intermediate case corresponds to “liquid society”. In physics, liquid is characterised with low-distance order and long-distance disorder. Models based on local interaction satisfy this property. This is also similar to economics of networks, which is now becoming increasingly popular. Liquid society may contain spontaneously emerging chains of polymers.13) It usually takes place in moderately rich societies with some degree of individual freedom. Strong state and little individual wealth prevents this state from emergence. Mafia, at least in the sense of unofficial power different from state, usually do not emerge in very poor and very rich society, and when state is extremely strong. Interaction between agents of different types can be neutral, positive or negative. In the paper by Aruka and Mimkes (2006) six real structures of agent interaction are introduced: segregation, aggression, partnership, hierarchy, democracy and global
The economic concept of agents does not specify whether agent can be given by individual, household, firm, etc. Usually it assumes that agents are identical, which suggests that individuals are considered. It is also problematic to talk about unique utility for a group of agents. That is why economic individuals resemble atoms in physics, while household–molecules. 13) Examples of these polymer structures contain mafias and clans.
12)

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structure. Classical economics deals more with either no interaction (everybody maximizes own utility, gas-type society) or negative interaction (an attempt to gain at the expense of partner is common in games considered by economists). It is important to mention that a theory of positive interaction (altruism) is also finding its way among new trends of economic theory (see Bowles, 2003). 5. 5.1 Extensions of Neoclassical Economics: Mathematical Formalization Post-Liberal Economics: Necessity to build a link between main fundamental ideologies Globalisation process sets forward a problem of coexistence in the world with different ideologies. In order to understand how multiplicities of social structures can coexist, interact and transform into each other, it is necessary to have common language for expression of global states of economy. Especially this was important before transition. How was it possible to talk rationally about it, if there was no economic language to describe transition path (it started in one society and had to end in another)? Contribution to political science is also on agenda. This section aims to introduce some mathematical elements of formalization of the problem. Bowles and Gintis (2005) show that it is difficult to sustain cooperation in n-person public good games, like food-sharing, co-insurance, common defence, information sharing, by means of standard tit-for-tat and other reciprocal strategies. The contemporary study of human behaviour has documented a large class of social behaviours inexplicable in terms of reciprocal altruism. Laboratory and field experiments show that other-regarding preferences cause robust cooperative behaviour, even in anonymous setting. These finding put the investigation of non self-regarding preferences into the agenda. Almost all microeconomic textbooks (with a nice exception of Bowles 2003) exclude them from consideration. The link between a dominant economic theory (neoclassical economics) with the ideology of liberalism is obvious, but is not discussed by economists. While Marxism was the major ideology for substantial part of the world during several decades of the 20th century, there was no attempt to translate its paradigms into mathematical language and to compare them with those from neoclassical economics. Here it is important to make a distinction between works of K. Marx and Marxism as one of important ideologies. In its practical implementation (Soviet Union, Eastern European countries, China) it lead to low income dispersion and caring about the utility of the poorest members of the society. This section aims to suggest a direction in mathematical
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economics, along which such a link can be done. 5.2 Preferences Despite significant ideological difference with neoclassical economics (and not less with Marxist or other alternative), I will follow the formal canons of neoclassics and start with assumptions and mathematical formulations. In order to cross the natural border of neoclassical economics and to build a formal link with formal economics, describing alternative social structures (nationalism, Marxism), it makes sense to extend individualistic utility function, in order to capture some altruism, or care about social utility. The social welfare functions are studied in public economics and normally include a wide spectrum of utilities formally captured by the formula
 Usoc  

∑ i  a U0,i  

1/ a

,

(1)

where a [0,1]. In the limit case, a 1, we get utilitarian social indifference curve:
Usoc |a
1

∑U i 0,i

. Without special justification at the moment, we will consider this

social utility to correspond to nationalist society. Consider as an alternative Rawlsian social indifference curve, formally given by the wealth of the poorest member of society: Usoc|a
0

mini U0,i . This concept is very close to Marxian paradigm, since in this case

equalization of income of all members of society brings the highest social welfare. The basic difference of nationalist society from Marxist society is that wealth inequality in nationalist state does not generate envy, and all agents are better off if some members of their nation become richer. The next step is a formal link between individualistic and social theories. Let us make formal assumptions.14) Assumption 1 Individual utility in a nationalist society is a weighted sum of own utility plus the sum of utilities of all members of the nation:
Ui U0,i β

∑U j 0,i .

(2)

These assumptions assume some level of altruism which is also studied by economists. We do not focus the attention here on the extent of this altruism (family level, nation level or global level). Every level can generate some structures of different order, and we focus on a country level only in order to use minimal mathematical complexity.

14)

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Assumption 2 Individual utility in Marxist society is given by another weighted sum:
Ui U0,i β min U0, j . j (3)

Corollary 1 Both nationalist and Marxist societies, in contrast to liberal individualistic society, assume some level of altruism, since b 0. Corollary 2 These utilities allow for some (nonlinear) interaction between members of the society, which normally15) gives rise to spontaneous emergence of some state-type structures, which can become a separate subject of action and not necessarily act in line with the preferences of all society members. On the other hand, liberal principle, under certain condition16) considers state as something external, destroying Pareto optimality which spontaneously emerges on liberal market. Corollary 3 The distribution of wealth matters for both nationalist and Marxist societies, while it does not matter for liberal society, because the latter has no nonlinearities in market interactions. This issue will be studied further. This is only the first step of mathematical formalization. It is based on existing concept of social utility (see Stiglitz, 1988), introduction of second dimension in individual preferences (idea of McClintock (1978)) and coexistence of three main ideologies (liberalism, nationalism and Marxism). We can see that neoclassical economics based on liberal principles is an asymptotic limit of nationalist or Marxist society, for b →0. It shows also why altruism is not included in neoclassical agenda: it gives rise to spontaneous emergence of state-type structures through preferences. But historically one can deal with existing state. One can remember how aggressively the state was destroyed in the former Soviet Union: before 1990 it controlled the production of almost all output, while in 1999 the state controlled less than 20% of GDP, which was an overshooting not only with respect to EU countries (with about 50%) but also USA (with about 30%). 5.3 Scale economies and externality effects The emergence of stable structures in physics occurs through potential of interaction.
15) 16)

This is a result of synergetics. No externalities, perfect information, etc — see Stiglitz (1988) for details.

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Generally, the energy of the system is not equal to sum of energies of separate parts but is given by:
E( system)

∑E i i

E(interaction).

(4)

The difference represents interaction. In economic language, it is externality. Economic models are mostly linear, i.e. they ignore interaction potential. The theory of firm in its part related to its spontaneous emergence, is not a part of modern economic theory. But it is clear that externality effects play role here. Externalities for labour Consider a production function with labour being the only input: Y f(L). Since labour is not infinitely divisible, consider self-employment as a firm with minimal quantity of labour. If technology is such that joint productivity of 2 workers is higher than sum of their productivities if they work separately, Y(2) 2Y(1), we have positive externality, or increasing returns to scale (IRS) effect to labour input in technology, and thus a potential for cooperation. As is shown in Yegorov (2001b, 2005a), the distribution of output for this technology is not obvious, and there may be contradictions between individual and group goals if we base conclusions on standard microeconomic principles. Modern game theory focuses too much on the bargaining problem. It makes sense to consider the case when bargaining would not emerge at all, i.e. individual optimisation will coincide with group optimisation. But if preferences are altruistic (of type (2)), there might be some range of parameters b so that there is no contradiction. Externalities for capital Now consider a technology with capital K as unique input. Assume that agents’ individual wealth, W, is an upper limit for capital that they can use for investment. Consider technology Y g(K), with g of IRS-DRS type. Then, at some level of K K*, the average capital productivity Y/K is maximized. If the total capital in society with N agents is KN, then it is socially optimal to split it into M firms, each of size K* KN /M. Now consider individual investment decisions. For low W, several agents need to cooperate to start a firm with K*. In a rich society individual may own a firm.17) If wealth grows, less cooperation is required, and society becomes more atomised. This is completely in line with the discussion about the role of temperature in society provided above.
17) This is more applicable for agriculture, with small farms, and necessity to cooperate for poorer people.

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5.4

Local cooperation leading to emergence of ethnic group

The role of altruism in preferences is important for many reasons. Some of them have been discussed in the book of Bolwes (2003). Here an example is provided. It has two goals: a) to demonstrate that altruism can bring more stability to the concept of equilibria and to lead to more robust structures, b) to explain possible mechanism of emergence of ethnic group. The idea of the model is based on the stylised fact about cooperation inside local communities, along to their suspicion to a stranger. The border of a community may be different: some people put it on a broad family, some on nation, there also exist internationalists, with altruistic attitude towards all human beings. It is clear that altruistic component plays an important role in such formations, as well as the link between nation and particular area on geographic map. The goal of this model is to propose a procedure leading to an emergence of such structures. Consider uniformly populated landscape, where agents can be put on a lattice (in discrete model) or occupy the space with a uniform population density. Twodimensionality and geographical relief are not very important at this stage. Thus, it is assumed that agents live on a line, each occupying a particular location x. Geographic dimension is not a unique dimension in this model. Assume also cultural difference (language, habits, traditions, religion), measured by a function h(x), which is assumed to be slowly varying with spatial coordinate: |h (x)| Local interaction and altruism In order to model interaction, we assume that initially agents are playing prisoner’s dilemma game with their neighbours. The payoffs are given by the matrix18) (Table 1):
Table 1. Game for U L U D (3, 3) (4, 0) R (0, 4) (1, 1)

1.

This game has bad (not efficient) Nash equilibrium (1, 1) in a standard framework of preferences. Now assume that both agents value not only their utility Ui , but utility of their partner as well (Table 2):
18)

The payoffs are chosen just for illustration

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Table 2. Game for V L U D R

(3(1 a ), 3(1 a ) ) (4a , 4) (4, 4a ) (1+a , 1+a )

V1 U1 a U2,V2 U2 a U1,

(5)

where a (0,1) — coefficient of altruism. The new game for V is given by the following table of payoffs. Depending on a , we can get a shift to more efficient equilibrium UL. We need a 1/3 to have such a shift. Radius of cooperation Let us assume that the level of altruism depends negatively on total distance between any pair of agents,19) d d12 mD x D h. This can be a combination of geographical and cultural distances. Historically, people did not move a lot,20) and geographical proximity implied cultural and religious proximity. Suppose that a 1/(1 d ). Then for d (0,∞) we have a (0,1). We immediately arrive to spatial pattern of cooperation. In our game people with distance d d* 2 would select efficient equilibrium. Translation into normal language would mean that “local communities play games cooperatively across them, but may be noncooperative with strangers”. This behaviour can be easily observed in some modern cultures that have kept traditions (Greece or Japan, for example). So far, we have explained why an agent would treat his local community better than strangers. But we have not explained, how nations, with much higher radius of territorial distance (R d*), would form a cluster of cooperation. We need to describe the mechanism of spatial propagation of local interaction, which at the same time ends at some border. Such borders are usually determined by either language or religious

Here m 0 is a parameter, which can be used for setting different weights for geographical and cultural differences. 20) In the sense that a small fraction of population migrated on long distances during their lifetime. Only recently overall migration increased significantly.

19)

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differences.21) Travellers Now assume that agents can travel, but their frequency of travel declines with distance exponentially. In other words, his probability to play a game with an agent at the geographical distance x is P(x) l e l ,x
∞

. Such a specification satisfies the necessary 1. In other words, agents almost neglect

condition for probability distribution: ∫0 P(x)dx 1. At the same time we will consider factor m to be a small parameter: m geographical distance and look only at cultural. Still, we cannot take geography out of the model, since it defines the pattern of travel. We also assume that initially agents were grown in a cooperative neighbourhood and got used to it when they became adults and started to travel. Finally, we assume that agents cannot measure cultural difference before interaction but can observe it through response. They can adapt their behaviour in two ways: a) they reverse cooperative to non-cooperative behaviour, if the payoff (in V!) becomes smaller than for alternative strategy; b) they travel less frequently to the direction where they have observed non-cooperative behaviour. Propagation of cooperation in space Without focusing on initial emergence of cultures and languages, we will consider spatial heterogeneity, characterized by function h(x), as given. Clearly, it has areas of slow variation (dialects, for example) and sharp borders, where transition occurs over small geographical distance D x. Define the area with no sharp differences in culture as prenation area. As people increased their mobility (and this happened historically with the development of transportation), parameter l declined. Agents started to cooperate in a broader neighbourhood, and they did not learn to reverse their behaviour unless they lived close to cultural border, and had high fraction of communications with different culture, which has resulted in suboptimality of cooperative behaviour. By learning to move there less frequently, they managed not to reverse initial strategy of cooperation, which finally has covered all pre-nation area. This is how nations could have formed.

21) Holland and Belgium represent a good example. Belgium is not homogeneous, with Flemish (almost Dutch) language spoken on the North and French in the South. At the same time, it is religiously more unique, since the border between Catholic and Protestant religions approximately coincides with the border between two countries. This shows more important role of religion in comparison with language, in defining historical borders of a country. However, often the difference of only one factor is sufficient for separations. We can observe a variety of languages and religions inside one country for former empires, which worked as an external force to put together communities that would segregate otherwise.

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6.

Applications

The goal of this section is to describe the directions where this philosophy of research can be applied. It is impossible to predict now all fruitful applications, but it makes sense to mention some of them. Some elaboration is done with the concept of wealth distribution and stability conditions for liberal society. The final subsection tries to bring some structure and interlinks between areas of research. 6.1 Where these models can be useful? Here the short agenda of interesting directions of future research is listed. It is believed that these social processes can be properly described by the methods discussed in this article. However, further elaboration can take substantial effort and time, and thus could be an agenda for future research. 1. Analytical description of transition process. The transition from centralized to market economy in the former Soviet Union started in 1992 with “shock therapy”. In the press it was argumented by welfare theorems from neoclassical economics about efficiency of emerging market equilibrium. However, the concepts of that theory were not applicable not only because lack of knowledge, lack of institutions, incomplete and asymmetric information (especially in the case of privatisation), but also because the transition itself is a disequilibrium process (and fast, shock, non-adiabatic transition especially) by definition, and the western economic school has never developed such disequilibrium theory. The use of some tools from physics allows to do this in principle, and although it is too late to apply results practically, this could be an important contribution to our understanding of modelling real economic processes. 2. Explaining historical paths of different social formations. behind it (a self-reinforcing loop: poor society tends to be a dictatorship which keeps it poor) and their right to exist. 4. Studying the role of state in economy and its link to level of freedom and richness. 6.2 The role of wealth distribution It is possible to predict the crucial difference between Marxism and nationalism, arising from the effect of wealth distribution. Empirically we know that nationalist or religious societies are much more tolerant to wealth inequality than those based on Marxist 3. Understanding the stability of different regimes and seeing economic reasons

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principles. But the structure of formulae in Assumptions 1,2 give exactly the same predictions. Suppose that wealth is distributed not equally but there is no way for costless redistribution. Then such redistribution would mean some decline of the second term in utility function of each member. For some members, non necessarily rich, but of middle class, this decline will overweight potential personal gain. Thus, a majority interested in such redistribution will not emerge. Consider now Marxist society. For it, any deviation from equality brings negative utility to each member. Suppose, for simplicity, that there are two levels of wealth: low w (fraction a ) and high w (fraction 1 a ), where a (0,1) but most likely to be closer to 1. Then the utility of poor is Up U0(w)(1 b ), while the utility of rich is Ur U0(W) b U0(w). For b high enough, even richer people would be personally interested in full equalization. Alternatively, for low b two classes will emerge, with all consequences predicted by Marxists. In the case of general distributions it is likely that low inequalities will not generate antagonism is either society, while for higher level, nationalist society is more tolerant and stable than Marxist. 6.3 The conditions of stability of liberal society While it is difficult to criticize the principles of liberal society (freedom, equality, brotherhood), its realization is often far from proclaimed principles.22) Usually liberal society self-reinforce the initial difference in endowments and skills among agents.23) The main reasons involve asymmetric access to credit (the rich can get it always and at lower interest rate than the poor) and more destabilizing effect of random shocks on households close to subsistence level. Thus, liberal principles does not guarantee “honest outcome” when every worker gets wage according to his productivity, and everybody can be an entrepreneur, with outcome depending on skills only. The natural political principle of liberal society is the majority voting scheme, with the main focus on median voter. Now let us turn to the physical principle of phase transitions described before. Suppose that the initially high role of state in relatively poor country was forcefully diminished, like it happened in Russia in 1990s. The liberalization has caused wealth polarization.24) If Marxist ideology had not been rapidly abandoned, this could have lead to emergence of classes with their struggle. The main ideological
As well as realized societies based on Marxist principles. The polarization across peasants initially endowed with almost equal slots of land after Russian revolution of 1917, by the year 1930. 24) I am not mentioning the increased role of mafia as another natural consequence of the decline of state role.
23) 22)

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competition was between nationalist and liberal idea. Consider the conditions for liberal paradigm to win this competition. The median voter was objectively worse off economically.25) With a monthly average income of about 100 USD and almost western prices (despite huge temporal variation of nominal average income in Russia between 1993–1999, the PPP adjusted income did not change much.) At such income level, gain from less pressure (more freedom) did not compensate for economic loss, and the composition of these two parameters naturally corresponded to “solid” or “liquid”, but not “gas” state. The richer 10% were naturally supporting “gas” (liberal) state, but they needed to use some manipulation of public opinion with mass media, to form an illusion of social agreement on liberal state. On the other hand, the increase of nationalistic ideas and the role of religion worked towards higher popularity of nationalist (solid) state among medium voters. Since “solid” and “gas” state cannot coexist (while solid and liquid can), some liquid (better to say, polymer) structures have started to emerge in business. They can be formally studied by economics of networks. 6.4 Link with research on structural economics, science of transition and political science In order not to get lost in the variety of fundamental cornerstones of future econo-physic theory and variety of its applications, it makes sense to impose some preliminary structure. Structural economics Structural economics is one of the corner stones of this new theory. It studies selfemergence of structures in a form of spontaneously united group of agents, or network (with or without topology of interlinks). Space is an important but not unique factor of self-organization (Yegorov, 2001a), which also comes from nonlinear interaction of initially identical elements (for example, through production function, locally having IRS; see Yegorov (2001b, 2005a). Economics of transition To study economics of transition theoretically, one needs a formal link between different regimes first. The proposed utility function and the analogies of phase transitions in physics represent one possibility to build such models. Modelling transition is a fundamentally difficult task. While transition in a narrow sense (as shift of capital and labour to new sectors during industrialization) can follow an optimal path, transition of Big Bang type is unpredictable in details in principle. In the chapter 8 of Faber et al.
25) By observations, only about 10 % of population had economic gain from transition, although the majority recognize the gain in individual freedom previously suppressed by state.

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(1996) the model of Big Bang, describing the behaviour of universe in the first few seconds after its emergence, is discussed. It is fundamentally unpredictable process, as even some fundamental physical constants could take different asymptotic values depending on the path of the process. Transition from post-communist to market economies included simultaneous shift in ideologies, changing of legal structure, privatisation, mostly on the background of hyperinflation. There have been many unpredictable novelties, and the complexity is likely to be of higher order, than simple multiplicity of equilibria. It could also involve a sequence of unforcastable structural changes along the path of convergence to new equilibria. While it is generally impossible to describe this process mathematically as a deterministic path, the application of some evolutionary concepts is important in understanding its structure. The concept of self-emergence of structures and their stability is as important as the concepts of “genotype” and “ecological niche” in theoretical biology. But obtaining unified mathematical model, that is able to describe the social system dynamics both is non-liberal and liberal framework, which was discussed above, is of crucial importance before any practical modelling takes place. Political science The emergence of stable structures and studying the limits of their stability can give some insights for policy makers. If a particular state is natural, no external reforms can change its structure in the long run. “Heating” society involves both the decline of the state role together with wealth increase (external aid). For example, decline of state’s role without significant increase of wealth of median voter, cannot assure a foundation for a stable democratic society. And the example of Russia (where an attempt to compensate the lack of aid by excess destruction of state, which did not finally succeed in establishing stable irreversible democracy), in contrast with Eastern and Central European countries,26) is a good illustration. 6.5 About social diffusion, vertical and horizontal Let us start from physics. Diffusion is the process of penetration of elements of one nature into the media of different nature. For example, two gases were separated and now they are in contact. Molecules of one of them will penetrate into the other. The process of diffusion is described by diffusion equation, which shows that the total amount of penetrated molecules and the average distance of penetration grow over time but non-linearly. The situation with liquids is different. If we have a mixture of different liquids with different densities, their location is ordered with time. This principle is used
26)

I mean mostly Hungary, Poland, Czech Republic.

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Y. YEGOROV

in rectification columns to separate oil into fractions. If we mix oil with water, it will occupy the upper part of the volume in gravity field. The reason that prevents diffusion in the case of liquid is related to the interaction field between the molecules of the same type: other molecules do not allow one molecule to escape, we have some kind of collective phenomenon. Can we find interesting analogies in social life? Yes. Let personal wealth be an analogy of individual energy, while the interaction forces are represented by some formal and informal laws (traditions, collective rules, etc). If these forces are weak, we have liberal society (an analogy of gas), but if they are strong, we have a traditional society. In traditional societies it is difficult to make an action without mental self-reference to the opinion of collective, while in liberal societies individuals are independent on this opinion. Consider the process of mobility across social classes. In traditional society, a person without proper genealogy could not become an aristocrat, independently on the level of his wealth. This was the reason of bourgeois revolutions, which improved social status of the “third class”. In modern liberal societies, entry to another social group is more easy, but we also have some “closed societies”, a ticket to which cannot by bought. The described case is an example of vertical social diffusion, which is more easy in gas-type (liberal) society and more difficult in liquid-type (traditional) society. Another example is related to horizontal diffusion, and it can be easier explained using military example. In the time of the Second World war the fronts separating two armies were well defined in space, and penetration (diffusion) was a difficult task, at least at mass level. Now, in the epoque of terrorist attacks, such diffusions play an increasing role in the strategy of a conflict. The previous society was more of liquid type, with more control over actions of each individual, while now societies are more liberal, and this control became less. Gas-type diffusion in modern societies became easier for individuals. The examples considered above show how the analogies between physics and social life can be used for studying particular questions of social organization and movement. 7. Conclusive Remarks

The method of introducing physical methodology into economic modelling with keeping most of economic assumptions allows to describe much richer class of socio-economic phenomena. In particular, it is possible to deal with emergence of different structures and study different social orders by common mathematical tools. This paper only sets up
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some potentially fruitful directions of research. It is shown that market force in not a unique interaction between economic agents. Non-market interaction include deviation from self-regarding preferences that can explain the emergence of stable structures (like groups, nations and countries). Moreover, movement along these lines allow to explain the societies based on alternative ideologies (Marxism and nationalism). Spatial forces represent another self-organizing social principle that is complementary to “invisible hand”. This explains the importance of regional science and urban economics. Scale economies can also lead to endogeneous group formation. In combination with transport costs they give rise to a wide range of stable heterogeneous structures in space. The analogy between different phases of matter (solid, liquid, gas) and social orders with different levels of economic freedom is presented. It allows to provide a wider view on possible socio-economic structures and the order parameters (social analogies of temperature and pressure from physics) that are responsible for phase transitions between them. References
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Organization in Physics, Chemistry and Biology, Springer-Verlag, Berlin. Kara-Murza, S. (2002) Ideology and Her Mother Science (in Russian), Algorithm, Moscow, p. 256. Krishnan, R., J. Harris J. and N. Goodwin (eds) (1995) A Survey of Ecological Economics, Island Press, Washington D.C., p. 384. Kuhn, T. (1970) The Structure of Scientific Revolutions, University of Chicago Press, Chicago, p. 210. Mantegna, R. N. and H. E. Stanley (2000) An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press, Cambridge, p. 148. McClintock, C. (1978) “Social Values: Their Definition, Measurement and Development,” Journal of Research and Development in Education 12.1: 121–137. Parshev, A. (2001) Why Russia in not America? (in Russian), Moscow. Skirbekk, S. (2003) Dysfunctional Culture, “MIK”, Moscow, p. 270. [Translated in Russian from Norwegian] Stiglitz, J. (1988) Economics of the Public Sector, W. Norton Co., p. 692. Stocker, R., D. Green and D. Newth (2000) “Connectivity, Cohesion and Communication in Simulated Social Networks,” Proceedings of 4th Japan-Australia Joint Workshop on Intelligent and Evolutionary Systems, Shonan Village, Japan, 31/10–2/11/2000. Weidlich, W. (2002) Sociodynamics — A Systematic Approach to Mathematical Modelling in Social Sciences, Harwood Academic Publishers. — (2006) “Intentions and Principles of Sociodynamics,” Evolutionary and Institutional Economic Review 2.2: 161–165. Yegorov, Y. (1998) “Increasing Returns to Scale and Transport Cost”, Mimeo, UPF, Barcelona. — (2001a) “Structural Economics”. CEU, Mimeo, Budapest. — (2001b) “Competition of Self-Organized Groups”, CEU, Mimeo, Budapest. — (2005a) “Dynamically Sustainable Economic Equilibria as Self-Organized Atomic Structures,” in M. Salzano and A. Kirman (eds) Economics: Complex Windows, SpringerVerlag Italia, pp.187–199. — (2005b) “Role of Density and Field in Spatial Economics,” in Y. Lawrence (ed) Contemporary Issues in Urban and Regional Economics, Nova Science Publishers, pp. 55–78.

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