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Title: Statistical Physics and Thermodynamic approach to Economy Semester: Winter (1st)
Tutor: Theodoros Karakasidis, Associate Professor


Course outline:

The probabilistic approach to economic variables. The statistical mechanics of Money.  The Levy Statistics in Economy. The Ising Model in Economy. The Boltzmann-Gibbs distribution of energy, conservation of money.  The Boltzmann-Gibbs distribution of money.  Models with debt. Data and Models for Income Distribution. A Thermodynamic Formulation of Economics, the First Law of Economics, the Second Law of Economics-Entropy and Production Function-Pressure. Personal Freedom-Entropy in Economics. The Carnot Process of Production and Trade.


This course aims to be an introduction to Statistical Physics and Thermodynamic approach in Economy and their applications of laws and distributions of Statistical physics and Thermodynamics to Economic systems. It aims also to help students understand the role of debt, monetary profit, and money in open and closed thermodynamic cycles.

Learning objectives:

The objective of this Course is to relate closed economic system, where money is conserved by analogy with energy, with the laws of Thermodynamics and Statistical Physics. The equilibrium probability distribution of money must follow the exponential Boltzmann–Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. The students will be able to demonstrate how the Boltzmann– Gibbs distribution and other distributions, emerges in computer simulations of economic models. Then they will consider a thermal machine, in which the difference of temperatures allows one to extract a monetary profit. Also they will recognize the role of debt, and models with broken time-reversal symmetry for which the Boltzmann–Gibbs law does not hold.

On completion of this module, students are expected to be able to:

¬ Understand correlation of Economic systems with the Laws of Thermodynamic and Statistical Physics

¬ Apply the Boltzmann–Gibbs law to an economic system

¬ Simulate in long time scale Economic system that obey to Thermodynamic laws

¬ Understand the limits within which are valid the models and approaches of Thermodynamics and Statistical Physics in Economy.

Suggested for further reading:

1. P. Cockshott, A. F. Cottrell, G. J. Michaelson I. P. Wright and V. M. Yakovenko, “Classical Econophysics”, Routledge advances in experimental and computable economics Edited by K. Vela Velupillai National University of Ireland, Galway and Francesco Luna International Monetary Fund (IMF), Washington, USA, 2009.

2. J. Bryant, “Thermoeconomics: “A Thermodynamic Approach to Economics” (Second Edition)”, Vocat International Ltd, 2011.

3. C. Biely, “Statistical Mechanics of Networks: Applications in Econophysics”, VDM Verlag Dr. Muller Aktiengesellschaft & Co. KG, 2008.

4. R. Kummel, “The Second Law of Economics: Energy, Entropy, and the Origins of Wealth (The Frontiers Collection)”, Springer, 2011.

5. M. Schulz, “Statistical Physics and Economics: Concepts, Tools and Applications (Springer Tracts in Modern Physics)”, Springer, 2003.

6. H. Aoyama, Y. Fujiwara, Y. Ikeda, H. Iyetomi and Wataru Souma “Econophysics and Companies Statistical Life and Death in Complex Business Networks”, Cambridge University Press.

7. V. M. Yakovenko, “Econophysics, Statistical Mechanics Approach to”, Encyclopedia of Complexity and Systems Science, Part 5, 2009

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