Andrés Salamanca holds a BSc. in Economics and a MSc. in Applied Mathematics from the National University of Colombia. Currently, he is a M1 student in Economics at TSE. His main research interests are within cooperative game theory and the applications of outof equilibrium statistical mechanics to the understanding of economic problems. *Email: asalamancal.tse@gmail.com Economic science has been influenced by physical concepts since its very beginning. A simple but prominent example is the enormous influence the book Éléments de Statistique, by the French physicist and mathematician Louis Poinsot, had on Leon Walras’s work. In Poinsot we find virtually the whole formal apparatus that Walras later employed in his Éléments d’Économie Politique Pure. Walras’s formulation of general equilibrium is nothing but a system of simultaneous and interdependent equations à la Poinsot with the introduction of an auctioneer a device that allows the match of supply and demand in a market of perfect competition. Other examples of the use of mechanical concepts and theories in economics have been analyzed by Mirowski (1999): (i) the lever rule by Nicolas Canard, (ii) gravitation theory by Stanley Jevons, and (iii) the minimum energy principle by Francis Edgeworth, among others. Irving Fisher in 1892 established an extensive relation of analogies and metaphors between mechanics and economics. According to Fisher (1991), while economic optimality corresponds to maximum profit, mechanical optimality corresponds to minimum energy.
As economic science is developing, theories and ideas inspired by physics are growing. Recent contributions have introduced in economics the possibility to treat analytically the issue of many heterogeneous and interacting agents and thus to microfound aggregate behavior without relying on the hypothesis of a representative agent. An example of these developments is the large research work carried out by the Santa Fe Institute, a transdisciplinary research community dedicated to enhancing the scientific understanding of complex social and physical systems. Achievements of this sort have shown that economics must depart from the mechanical equilibrium of the PoinsotWalras framework to the economics of equilibrium probability distributions, in which agents are constantly driven by disequilibrium forces and the complexity of the system pervades the social behavior. As a complex macroscopic thermodynamic system is described by the “average” behavior of the very large numbers of its microscopic constituents through statistical mechanics, macroeconomic variables must be understood by the result of many interacting individuals. Complex systems theory analyses the way in which the interaction of a large number of parts of a system gives rise to aggregate behaviors and how the system as a whole interacts with its components. Mathematical tools of complex systems models are developed from statistical mechanics, dynamical systems theory, graph theory, game theory, network theory and computation theory, among others. A fundamental property of complex systems is emergence, i.e., aggregate patterns created from “simple” interactions. Other features of complex systems are selforganization, evolution, adaptation, nonlinear dynamics, network structures, nonstationarity and disequilibrium. It has been argued by Saari (1995), that complexity is ubiquitous in economic problems, since (i) the economy is inherently characterized by the direct interaction of individuals, and (ii) these individuals have cognitive abilities so that they form expectations on aggregate outcomes and base their behavior upon them. By contrast, the adoption of the classical mechanics into economics has led to a reductionist approach in the analysis of the difference between micro and macro. Aggregation is carried out by summing up market outcomes; therefore, the dynamics of the economic system is nothing but a summation of the individual dynamics. Considerations about the interdependencies between the agents and the aggregate properties of the system are driven out. Macroeconomic theory fails to realize the emergence of complex structures from simple individual behaviors. The application of mechanical statistics to economics has provided important insights into traditional problems of economic theory; one prominent example is the study of the income distribution among individuals in an economy. Empirical research on data for different societies has identified a powerlaw tail (Pareto law) and a lognormal bulk of the income distribution. The emergence of this “scaling” property in the income cannot be understood from the customary tools of traditional economic analysis. In contrast, for physical systems the fundamental law of equilibrium is the BoltzmannGibbs law, which is in a precise mathematical relation to power laws when the measurables are presented on a logarithmic scale. BoltzmannGibbs law is obtained by Dragulesco and Yakovenko (2000) for a close economy when the trading process between economic agents is completely random. Regarding the fat tail in the income distribution, several researchers have obtained Paretolike behavior using approaches such as random savings (Chaterjee et al. 2004). As much as classical economics imported Lagrangian models from classical physics and financial economics built on the model of Brownian motion imported from physics (the socalled BlackScholes model), so, econophysics wants to model economic phenomena using analogies taken from modern condensed matter physics and its associated mathematical tools and concepts. Also, whereas mainstream microeconomics is based on the rational behavior of individuals, econophysics focuses on interactions between actors that lead to the emergence of statistical macrolaws typically power laws instead of Gaussian ones as expected in classical economics (Schinckus, 2010). The official birth of the term “econophysics” was coined by Harry Eugene Stanley in 1996. Econophysics presents itself as a new way of thinking about economic and financial systems. Some References Chatterjee, A., Chakrabarti, B.K. and Manna, S.S. (2004). “Pareto law in a kinetic model of market with random saving propensity”, Physica A, 335, 155163. Dragulescu, A.A. and Yakovenko, V.M. (2000). “Statisti cal mechanics of money”, European Physical Journal B, 17, 723729. Fisher, I. (1991). Mathematical Investigations in the Theory of Value and Prices. 1892. Reprint, Augustus M. Kelley, Fairfield, NJ. Mirowski, P. (1999). More Heat than Light. Econom ics as Social Physics, Physics as Nature’s Economics. Cambridge University Press, New York.
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