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Complex Systems in Finance and Econometrics pp 247–273Cite as

Econophysics, Statistical Mechanics Approach to

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Article Outline

Glossary

Definition of the Subject

Historical Introduction

Statistical Mechanics of Money Distribution

Statistical Mechanics of Wealth Distribution

Data and Models for Income Distribution

Other Applications of Statistical Physics

Future Directions, Criticism, and Conclusions

Bibliography

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Notes

  1. 1.

    However, when \( \Delta m \) is a fraction of the total money \( m_i+m_j \) of the two agents, the model is time-reversible and has an exponential distribution, as discussed in Sect. “The Boltzmann–Gibbs Distribution of Money”.

Abbreviations

Probability density :

P(x) is defined so that the probability of finding a random variable x in the interval from x to \( x+{\text{d}}x \) is equal to P(x) dx.

Cumulative probability :

C(x) is defined as the integral \( C(x)=\int_x^\infty P(x) {\text{d}}x \). It gives the probability that the random variable exceeds a given value x.

The Boltzmann–Gibbs distribution :

gives the probability of finding a physical system in a state with the energy ε. Its probability density is given by the exponential function  (1).

The Gamma distribution :

has the probability density given by a product of an exponential function and a power-law function , as in (9).

The Pareto distribution :

has the probability density \( P(x)\propto 1/x^{1+\alpha}\) and the cumulative probability \( C(x)\propto 1/x^\alpha \) given by a power law. These expressions apply only for high enough values of x and do not apply for \( x \to 0 \).

The Lorenz curve :

was introduced by American economist Max Lorenz to describe income and wealth inequality. It is defined in terms of two coordinates x(r) and y(r) given by (19). The horizontal coordinate x(r) is the fraction of the population with income below r, and the vertical coordinate y(r) is the fraction of income this population accounts for. As r changes from 0 to ∞, x and y change from 0 to 1, parametrically defining a curve in the \( (x,y) \)-plane.

The Gini coefficient :

G was introduced by the Italian statistician Corrado Gini as a measure of inequality in a society. It is defined as the area between the Lorenz curve and the straight diagonal line, divided by the area of the triangle beneath the diagonal line. For perfect equality (everybody has the same income or wealth) \( G=0 \), and for total inequality (one person has all income or wealth, and the rest have nothing) \( G=1 \).

The Fokker–Planck equation :

is the partial differential equation (22) that describes evolution in time t of the probability density P(r, t) of a random variable r experiencing small random changes \( \Delta r \) during short time intervals \( \Delta t \). It is also known in mathematical literature as the Kolmogorov forward equation . The diffusion equation is an example of the Fokker–Planck equation.

Bibliography

Primary Literature

  1. Chakrabarti BK (2005) Econophys-Kolkata: a short story. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of Wealth Distributions. Springer, Milan, pp 225–228

    Chapter  Google Scholar 

  2. Carbone A, Kaniadakis G, Scarfone AM (2007) Where do we stand on econophysics? Phys A 382:xi–xiv

    Article  Google Scholar 

  3. Stanley HE et al (1996) Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics. Phys A 224:302–321

    Article  Google Scholar 

  4. Mantegna RN, Stanley HE (1999) An introduction to econophysics: correlations and complexity in finance. Cambridge University Press, Cambridge

    Book  Google Scholar 

  5. Galam S (2004) Sociophysics: a personal testimony. Phys A 336:49–55

    Article  Google Scholar 

  6. Galan S, Gefen Y, Shapir Y (1982) Sociophysics: a new approach of sociological collective behaviour. I. Mean-behaviour description of a strike. J Math Soc 9:1–13

    Article  Google Scholar 

  7. Stauffer D (2004) Introduction to statistical physics outside physics. Phys A 336:1–5

    Article  Google Scholar 

  8. Schweitzer F (2003) Brownian agents and active particles: collective dynamics in the natural and social sciences. Springer, Berlin

    Google Scholar 

  9. Weidlich W (2000) Sociodynamics: a systematic approach to mathematical modeling in the social sciences. Harwood Academic Publishers, Amsterdam

    Google Scholar 

  10. Chakrabarti BK, Chakraborti A, Chatterjee A (eds) (2006) Econophysics and sociophysics: trends and perspectives. Wiley-VCH, Berlin

    Google Scholar 

  11. Ball P (2002) The physical modelling of society: a historical perspective. Phys A 314:1–14

    Article  Google Scholar 

  12. Ball P (2004) Critical mass: how one thing leads to another. Farrar, Straus and Giroux, New York

    Google Scholar 

  13. Boltzmann L (1905) Populäre Schriften. Barth, Leipzig, p 360

    Google Scholar 

  14. Austrian Central Library for Physics (2006) Ludwig Boltzmann 1844–1906. ISBN 3-900490-11-2. Vienna

    Google Scholar 

  15. Pareto V (1897) Cours d'Économie Politique. L'Université de Lausanne

    Google Scholar 

  16. Mirowski P (1989) More heat than light: economics as social physics, physics as nature's economics. Cambridge University Press, Cambridge

    Google Scholar 

  17. Majorana E (1942) Il valore delle leggi statistiche nella fisica e nelle scienze sociali. Scientia 36:58–66 (English translation by Mantegna RN in: Bassani GF (ed) (2006) Ettore Majorana Scientific Papers. Springer, Berlin, pp 250–260)

    Google Scholar 

  18. Montroll EW, Badger WW (1974) Introduction to quantitative aspects of social phenomena. Gordon and Breach, New York

    Google Scholar 

  19. Föllmer H (1974) Random economies with many interacting agents. J Math Econ 1:51–62

    Google Scholar 

  20. Blume LE (1993) The statistical mechanics of strategic interaction. Games Econ Behav 5:387–424

    Article  Google Scholar 

  21. Foley DK (1994) A statistical equilibrium theory of markets. J Econ Theory 62:321–345

    Article  Google Scholar 

  22. Durlauf SN (1997) Statistical mechanics approaches to socioeconomic behavior. In: Arthur WB, Durlauf SN, Lane DA (eds) The Economy as a Complex Evolving System II. Addison-Wesley, Redwood City, pp 81–104

    Google Scholar 

  23. Anderson PW, Arrow KJ, Pines D (eds) (1988) The economy as an evolving complex system. Addison-Wesley, Reading

    Google Scholar 

  24. Rosser JB (2008) Econophysics. In: Blume LE, Durlauf SN (eds) New Palgrave Dictionary of Economics, 2nd edn. Macmillan, London (in press)

    Google Scholar 

  25. Drăgulescu AA, Yakovenko VM (2000) Statistical mechanics of money. Europ Phys J B 17:723–729

    Google Scholar 

  26. Chakraborti A, Chakrabarti BK (2000) Statistical mechanics of money: how saving propensity affects its distribution. Europ Phys J B 17:167–170

    Article  Google Scholar 

  27. Bouchaud JP, Mézard M (2000) Wealth condensation in a simple model of economy. Phys A 282:536–545

    Google Scholar 

  28. Wannier GH (1987) Statistical physics. Dover, New York

    Google Scholar 

  29. Lopez-Ruiz R, Sanudo J, Calbet X (2007) Geometrical derivation of the Boltzmann factor. Available via DIALOG. http://arxiv.org/abs/0707.4081. Accessed 1 Jul 2008

  30. Lopez-Ruiz R, Sanudo J, Calbet X (2007) On the equivalence of the microcanonical and the canonical ensembles: a geometrical approach. Available via DIALOG. http://arxiv.org/abs/0708.1866. Accessed 1 Jul 2008

  31. Anglin P (2005) Econophysics of wealth distributions: a comment. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, New York, pp 229–238

    Chapter  Google Scholar 

  32. Lux T (2005) Emergent statistical wealth distributions in simple monetary exchange models: a critical review. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 51–60

    Chapter  Google Scholar 

  33. Gallegati M, Keen S, Lux T, Ormerod P (2006) Worrying trends in econophysics. Phys A 370:1–6

    Article  Google Scholar 

  34. Lux T (2008) Applications of statistical physics in finance and economics. In: Rosser JB (ed) Handbook of complexity research. Edward Elgar, Cheltenham, UK and Northampton, MA (in press)

    Google Scholar 

  35. Computer animation videos of money-transfer models. http://www2.physics.umd.edu/~yakovenk/econophysics/animation.html. Accessed 1 Jul 2008

  36. Wright I (2007) Computer simulations of statistical mechanics of money in mathematica. Available via DIALOG. http://demonstrations.wolfram.com/StatisticalMechanicsOfMoney. Accessed 1 Jul 2008

  37. McConnell CR, Brue SL (1996) Economics: principles, problems, and policies. McGraw-Hill, New York

    Google Scholar 

  38. Patriarca M, Chakraborti A, Kaski K, Germano G (2005) Kinetic theory models for the distribution of wealth: Power law from overlap of exponentials. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 93–110

    Chapter  Google Scholar 

  39. Bennati E (1988) Un metodo di simulazione statistica per l'analisi della distribuzione del reddito. Rivista Internazionale di Scienze Economiche e Commerciali 35:735–756

    Google Scholar 

  40. Bennati E (1993) Il metodo di Montecarlo nell'analisi economica. Rassegna di Lavori dell'ISCO (Istituto Nazionale per lo Studio della Congiuntura), Anno X 4:31–79

    Google Scholar 

  41. Scalas E, Garibaldi U, Donadio S (2006) Statistical equilibrium in simple exchange games I: methods of solution and application to the Bennati–Drăgulescu–Yakovenko (BDY) game. Europ Phys J B 53:267–272

    Article  Google Scholar 

  42. Mimkes J (2000) Society as a many-particle system. J Therm Anal Calorim 60:1055–1069

    Article  Google Scholar 

  43. Mimkes J (2005) Lagrange principle of wealth distribution. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 61–69

    Chapter  Google Scholar 

  44. Shubik M (1999) The theory of money and financial institutions, vol 2. MIT Press, Cambridge, p 192

    Google Scholar 

  45. Mandelbrot B (1960) The Pareto-Lévy law and the distribution of income. Int Econ Rev 1:79–106

    Article  Google Scholar 

  46. Braun D (2001) Assets and liabilities are the momentum of particles and antiparticles displayed in Feynman-graphs. Phys A 290:491–500

    Article  Google Scholar 

  47. Fischer R, Braun D (2003) Transfer potentials shape and equilibrate monetary systems. Phys A 321:605–618

    Article  Google Scholar 

  48. Fischer R, Braun D (2003) Nontrivial bookkeeping: a mechanical perspective. Phys A 324:266–271

    Article  Google Scholar 

  49. Xi N, Ding N, Wang Y (2005) How required reserve ratio affects distribution and velocity of money. Phys A 357:543–555

    Article  Google Scholar 

  50. Ispolatov S, Krapivsky PL, Redner S (1998) Wealth distributions in asset exchange models. Europ Phys J B 2:267–276

    Article  Google Scholar 

  51. Angle J (1986) The surplus theory of social stratification and the size distribution of personal wealth. Soc Forces 65:293–326

    Article  Google Scholar 

  52. Angle J (1992) The inequality process and the distribution of income to blacks and whites. J Math Soc 17:77–98

    Article  Google Scholar 

  53. Angle J (1992) Deriving the size distribution of personal wealth from ‘the rich get richer, the poor get poorer’. J Math Soc 18:27–46

    Article  Google Scholar 

  54. Angle J (1996) How the Gamma Law of income distribution appears invariant under aggregation. J Math Soc 21:325–358

    Article  Google Scholar 

  55. Angle J (2002) The statistical signature of pervasive competition on wage and salary incomes. J Math Soc 26:217–270

    Article  Google Scholar 

  56. Angle J (2006) The Inequality Process as a wealth maximizing process. Phys A 367:388–414

    Article  Google Scholar 

  57. Engels F (1972) The origin of the family, private property and the state, in the light of the researches of Lewis H. Morgan. International Publishers, New York

    Google Scholar 

  58. Patriarca M, Chakraborti A, Kaski K (2004) Gibbs versus non-Gibbs distributions in money dynamics. Phys A 340:334–339

    Article  Google Scholar 

  59. Patriarca M, Chakraborti A, Kaski K (2004) Statistical model with a standard Gamma distribution. Phys Rev E 70:016104

    Article  Google Scholar 

  60. Repetowicz P, Hutzler S, Richmond P (2005) Dynamics of money and income distributions. Phys A 356:641–654

    Article  Google Scholar 

  61. Chatterjee A, Chakrabarti BK, Manna SS (2004) Pareto law in a kinetic model of market with random saving propensity. Phys A 335:155-163

    Article  Google Scholar 

  62. Das A, Yarlagadda S (2005) An analytic treatment of the Gibbs-Pareto behavior in wealth distribution. Phys A 353:529–538

    Article  Google Scholar 

  63. Chatterjee S, Chakrabarti BK, Stinchcombe RB (2005) Master equation for a kinetic model of a trading market and its analytic solution. Phys Rev E 72:026126

    Article  Google Scholar 

  64. Mohanty PK (2006) Generic features of the wealth distribution in ideal-gas-like markets. Phys Rev E 74:011117

    Article  Google Scholar 

  65. Patriarca M, Chakraborti A, Germano G (2006) Influence of saving propensity on the power-law tail of the wealth distribution. Phys A 369:723–736

    Article  Google Scholar 

  66. Gupta AK (2006) Money exchange model and a general outlook. Phys A 359:634–640

    Article  Google Scholar 

  67. Patriarca M, Chakraborti A, Heinsalu E, Germano G (2007) Relaxation in statistical many-agent economy models. Europ Phys J B 57:219–224

    Article  Google Scholar 

  68. Ferrero JC (2004) The statistical distribution of money and the rate of money transference. Phys A 341:575–585

    Article  Google Scholar 

  69. Scafetta N, Picozzi S, West BJ (2004) An out-of-equilibrium model of the distributions of wealth. Quant Financ 4:353–364

    Article  Google Scholar 

  70. Scafetta N, Picozzi S, West BJ (2004) A trade-investment model for distribution of wealth. Physica D 193:338–352

    Article  Google Scholar 

  71. Lifshitz EM, Pitaevskii LP (1981) Physical kinetics. Pergamon Press, Oxford

    Google Scholar 

  72. Ao P (2007) Boltzmann–Gibbs distribution of fortune and broken time reversible symmetry in econodynamics. Commun Nonlinear Sci Numer Simul 12:619–626

    Article  Google Scholar 

  73. Scafetta N, West BJ (2007) Probability distributions in conservative energy exchange models of multiple interacting agents. J Phys Condens Matter 19:065138

    Article  Google Scholar 

  74. Chakraborti A, Pradhan S, Chakrabarti BK (2001) A self-organising model of market with single commodity. Phys A 297:253–259

    Article  Google Scholar 

  75. Chatterjee A, Chakrabarti BK (2006) Kinetic market models with single commodity having price fluctuations. Europ Phys J B 54:399–404

    Article  Google Scholar 

  76. Ausloos M, Pekalski A (2007) Model of wealth and goods dynamics in a closed market. Phys A 373:560–568

    Article  Google Scholar 

  77. Silver J, Slud E, Takamoto K (2002) Statistical equilibrium wealth distributions in an exchange economy with stochastic preferences. J Econ Theory 106:417–435

    Article  Google Scholar 

  78. Raberto M, Cincotti S, Focardi SM, Marchesi M (2003) Traders' long-run wealth in an artificial financial market. Comput Econ 22:255–272

    Article  Google Scholar 

  79. Solomon S, Richmond P (2001) Power laws of wealth, market order volumes and market returns. Phys A 299:188–197

    Article  Google Scholar 

  80. Solomon S, Richmond P (2002) Stable power laws in variable economies; Lotka-Volterra implies Pareto-Zipf. Europ Phys J B 27:257–261

    Article  Google Scholar 

  81. Huang DW (2004) Wealth accumulation with random redistribution. Phys Rev E 69:057103

    Article  Google Scholar 

  82. Slanina F (2004) Inelastically scattering particles and wealth distribution in an open economy. Phys Rev E 69:046102

    Article  Google Scholar 

  83. Cordier S, Pareschi L, Toscani G (2005) On a kinetic model for a simple market economy. J Statist Phys 120:253–277

    Article  Google Scholar 

  84. Richmond P, Repetowicz P, Hutzler S, Coelho R (2006) Comments on recent studies of the dynamics and distribution of money. Phys A 370:43–48

    Article  Google Scholar 

  85. Richmond P, Hutzler S, Coelho R, Repetowicz P (2006) A review of empirical studies and models of income distributions in society. In: Chakrabarti BK, Chakraborti A Chatterjee A (eds) Econophysics and sociophysics: trends and perspectives. Wiley-VCH, Berlin

    Google Scholar 

  86. Burda Z, Johnston D, Jurkiewicz J, Kaminski M, Nowak MA, Papp G, Zahed I (2002) Wealth condensation in Pareto macroeconomies. Phys Rev E 65:026102

    Article  Google Scholar 

  87. Pianegonda S, Iglesias JR, Abramson G, Vega JL (2003) Wealth redistribution with conservative exchanges. Phys A 322:667–675

    Article  Google Scholar 

  88. Braun D (2006) Nonequilibrium thermodynamics of wealth condensation. Phys A 369:714–722

    Article  Google Scholar 

  89. Coelho R, Néda Z, Ramasco JJ, Santos MA (2005) A family-network model for wealth distribution in societies. Phys A 353:515–528

    Google Scholar 

  90. Iglesias JR, Gonçalves S, Pianegonda S, Vega JL, Abramson G (2003) Wealth redistribution in our small world. Phys A 327:12–17

    Google Scholar 

  91. Di Matteo T, Aste T, Hyde ST (2004) Exchanges in complex networks: income and wealth distributions. In: Mallamace F, Stanley HE (eds) The physics of complex systems (New advances and perspectives). IOS Press, Amsterdam, p 435

    Google Scholar 

  92. Hu MB, Jiang R, Wu QS, Wu YH (2007) Simulating the wealth distribution with a Richest-Following strategy on scale-free network. Phys A 381:467–472

    Article  Google Scholar 

  93. Bak P, Nørrelykke SF, Shubik M (1999) Dynamics of money. Phys Rev E 60:2528–2532

    Google Scholar 

  94. Her Majesty Revenue and Customs (2003) Distribution of personal wealth. Available via DIALOG. http://www.hmrc.gov.uk/stats/personal_wealth/wealth_oct03.pdf. Accessed 1 Jul 2008

  95. Drăgulescu AA, Yakovenko VM (2001) Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States. Phys A 299:213–221

    Google Scholar 

  96. Klass OS, Biham O, Levy M, Malcai O, Solomon S (2007) The Forbes 400, the Pareto power-law and efficient markets. Europ Phys J B 55:143–147

    Article  Google Scholar 

  97. Sinha S (2006) Evidence for power-law tail of the wealth distribution in India. Phys A 359:555–562

    Article  Google Scholar 

  98. Abul-Magd AY (2002) Wealth distribution in an ancient Egyptian society. Phys Rev E 66:057104

    Article  Google Scholar 

  99. Kakwani N (1980) Income Inequality and Poverty. Oxford University Press, Oxford

    Google Scholar 

  100. Champernowne DG, Cowell FA (1998) Economic inequality and income distribution. Cambridge University Press, Cambridge

    Google Scholar 

  101. Atkinson AB, Bourguignon F (eds) (2000) Handbook of income distribution. Elsevier, Amsterdam

    Google Scholar 

  102. Drăgulescu AA, Yakovenko VM (2001) Evidence for the exponential distribution of income in the USA. Europ Phys J B 20:585–589

    Google Scholar 

  103. Drăgulescu AA, Yakovenko VM (2003) Statistical mechanics of money, income, and wealth: a short survey. In: Garrido PL, Marro J (eds) Modeling of complex systems: seventh granada lectures, Conference Proceedings 661. American Institute of Physics, New York, pp 180–183

    Google Scholar 

  104. Yakovenko VM, Silva AC (2005) Two-class structure of income distribution in the USA: Exponential bulk and power-law tail. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 15–23

    Chapter  Google Scholar 

  105. Silva AC, Yakovenko VM (2005) Temporal evolution of the ‘thermal’ and ‘superthermal’ income classes in the USA during 1983-2001. Europhys Lett 69:304–310

    Article  Google Scholar 

  106. Hasegawa A, Mima K, Duong-van M (1985) Plasma distribution function in a superthermal radiation field. Phys Rev Lett 54:2608–2610

    Article  Google Scholar 

  107. Desai MI, Mason GM, Dwyer JR, Mazur JE, Gold RE, Krimigis SM, Smith CW, Skoug RM (2003) Evidence for a suprathermal seed population of heavy ions accelerated by interplanetary shocks near 1 AU. Astrophys J 588:1149–1162

    Article  Google Scholar 

  108. Collier MR (2004) Are magnetospheric suprathermal particle distributions (κ functions) inconsistent with maximum entropy considerations? Adv Space Res 33:2108–2112

    Article  Google Scholar 

  109. Souma W (2001) Universal structure of the personal income distribution. Fractals 9:463–470

    Article  Google Scholar 

  110. Souma W (2002) Physics of personal income. In: Takayasu H (ed) Empirical science of financial fluctuations: the advent of econophysics. Springer, Tokyo, pp 343–352

    Google Scholar 

  111. Fujiwara Y, Souma W, Aoyama H, Kaizoji T, Aoki M (2003) Growth and fluctuations of personal income. Phys A 321:598–604

    Article  Google Scholar 

  112. Aoyama H, Souma W, Fujiwara Y (2003) Growth and fluctuations of personal and company's income. Phys A 324:352–358

    Article  Google Scholar 

  113. Strudler M, Petska T, Petska R (2003) An analysis of the distribution of individual income and taxes, 1979–2001. The Internal Revenue Service, Washington DC. Available via DIALOG. http://www.irs.gov/pub/irs-soi/03strudl.pdf. Accessed 1 Jul 2008

  114. Souma W, Nirei M (2005) Empirical study and model of personal income. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 34–42

    Chapter  Google Scholar 

  115. Nirei M, Souma W (2007) A two factor model of income distribution dynamics. Rev Income Wealth 53:440–459

    Article  Google Scholar 

  116. Ferrero JC (2005) The monomodal, polymodal, equilibrium and nonequilibrium distribution of money. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 159–167

    Chapter  Google Scholar 

  117. Clementi F, Gallegati M (2005) Pareto's law of income distribution: evidence for Germany, the United Kingdom, the United States. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 3–14

    Chapter  Google Scholar 

  118. Clementi F, Gallegati M, Kaniadakis G (2007) κ-generalized statistics in personal income distribution. Europ Phys J B 57:187–193

    Article  Google Scholar 

  119. Clementi F, Gallegati M (2005) Power law tails in the Italian personal income distribution. Phys A 350:427–438

    Article  Google Scholar 

  120. Clementi F, Di Matteo T, Gallegati M (2006) The power-law tail exponent of income distributions. Phys A 370:49–53

    Article  Google Scholar 

  121. Rawlings PK, Reguera D, Reiss H (2004) Entropic basis of the Pareto law. Phys A 343:643–652

    Google Scholar 

  122. Banerjee A, Yakovenko VM, Di Matteo T (2006) A study of the personal income distribution in Australia. Phys A 370:54–59

    Article  Google Scholar 

  123. Gibrat R (1931) Les Inégalités Economiques. Sirely, Paris

    Google Scholar 

  124. Kalecki M (1945) On the Gibrat distribution. Econometrica 13:161–170

    Article  Google Scholar 

  125. Champernowne DG (1953) A model of income distribution. Econ J 63:318–351

    Article  Google Scholar 

  126. Milaković M (2005) Do we all face the same constraints? In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 184–191

    Google Scholar 

  127. Takayasu H, Sato AH, Takayasu M (1997) Stable infinite variance fluctuations in randomly amplified Langevin systems. Phys Rev Lett 79:966–969

    Article  Google Scholar 

  128. Kesten H (1973) Random difference equations and renewal theory for products of random matrices. Acta Math 131:207–248

    Google Scholar 

  129. Fiaschi D, Marsili M (2007) Distribution of wealth: theoretical microfoundations and empirical evidence. Working paper. Avialable via DIALOG. http://www.dse.ec.unipi.it/persone/docenti/fiaschi/Lavori/distributionWealthMicrofoundations.pdf. Accessed 1 Jul 2008

  130. Levy M, Solomon S (1996) Power laws are logarithmic Boltzmann laws. Int J Mod Phys C 7:595–751

    Article  Google Scholar 

  131. Sornette D, Cont R (1997) Convergent multiplicative processes repelled from zero: power laws and truncated power laws. J Phys I (France) 7:431–444

    Article  Google Scholar 

  132. Lydall HF (1959) The distribution of employment incomes. Econometrica 27:110–115

    Article  Google Scholar 

  133. Feller W (1966) An Introduction to Probability Theory and Its Applications, vol 2. Wiley, New York, p 10

    Google Scholar 

  134. Mimkes J, Aruka Y (2005) Carnot process of wealth distribution. In: Chatterjee A, Yarlagadda S, Chakrabarti BK (eds) Econophysics of wealth distributions. Springer, Milan, pp 70–78

    Google Scholar 

  135. Mimkes J (2006) A thermodynamic formulation of economics. In: Chakrabarti BK, Chakraborti A Chatterjee A (eds) Econophysics and sociophysics: trends and perspectives. Wiley-VCH, Berlin, pp 1–33

    Chapter  Google Scholar 

  136. Schelling TC (1971) Dynamic models of segregation. J Math Soc 1:143–186

    Article  Google Scholar 

  137. Mimkes J (1995) Binary alloys as a model for the multicultural society. J Therm Anal 43:521–537

    Article  Google Scholar 

  138. Mimkes J (2006) A thermodynamic formulation of social science. In: Chakrabarti BK, Chakraborti A, Chatterjee A (eds) Econophysics and sociophysics: trends and perspectives. Wiley-VCH, Berlin

    Google Scholar 

  139. Jego C, Roehner BM (2007) A physicist's view of the notion of “racism”. Available via DIALOG. http://arxiv.org/abs/0704.2883. Accessed 1 Jul 2008

  140. Stauffer D, Schulze C (2007) Urban and scientific segregation: the Schelling-Ising model. Avialable via DIALOG. http://arxiv.org/abs/0710.5237. Accessed 1 Jul 2008

  141. Dall'Asta L, Castellano C, Marsili M (2007) Statistical physics of the Schelling model of segregation. Available via DIALOG. http://arxiv.org/abs/0707.1681. Accessed 1 Jul 2008

  142. Lim M, Metzler R, Bar-Yam Y (2007) Global pattern formation and ethnic/cultural violence. Science 317:1540–1544

    Article  Google Scholar 

  143. Wright I (2005) The social architecture of capitalism. Phys A 346:589–620

    Article  Google Scholar 

  144. Defilla S (2007) A natural value unit – Econophysics as arbiter between finance and economics. Phys A 382:42–51

    Article  Google Scholar 

  145. McCauley JL (2006) Response to ‘Worrying Trends in Econophysics’. Phys A 371:601–609

    Article  Google Scholar 

  146. Richmond P, Chakrabarti BK, Chatterjee A, Angle J (2006) Comments on ‘Worrying Trends in Econophysics’: income distribution models. In: Chatterjee A, Chakrabarti BK (eds) Econophysics of stock and other markets. Springer, Milan, pp 244–253

    Chapter  Google Scholar 

  147. Rosser JB (2006) Debating the Role of Econophysics. Working paper. Available via DIALOG. http://cob.jmu.edu/rosserjb/. Accessed 1 Jul 2008

  148. Rosser JB (2006) The nature and future of econophysics. In: Chatterjee A, Chakrabarti BK (eds) Econophysics of stock and other markets. Springer, Milan, pp 225–234

    Chapter  Google Scholar 

  149. Kuznets S (1955) Economic growth and income inequality. Am Econ Rev 45:1–28

    Google Scholar 

  150. Levy F (1987) Changes in the distribution of American family incomes, 1947 to 1984. Science 236:923–927

    Article  Google Scholar 

  151. Internal Revenue Service (1999) Statistics of Income–1997, Individual Income Tax Returns. Publication 1304, Revision 12-99, Washington DC

    Google Scholar 

  152. Hayes B (2002) Follow the money. Am Sci 90:400–405

    Google Scholar 

  153. Ball P (2006) Econophysics: culture crash. Nature 441:686–688

    Article  Google Scholar 

Books and Reviews

  1. McCauley J (2004) Dynamics of markets: econophysics and finance. Cambridge University Press, Cambridge

    Book  Google Scholar 

  2. Farmer JD, Shubik M, Smith E (2005) Is economics the next physical science? Phys Today 58(9):37–42

    Article  Google Scholar 

  3. Samanidou E, Zschischang E, Stauffer D, Lux T (2007) Agent-based models of financial markets. Rep Prog Phys 70:409–450

    Article  Google Scholar 

  4. Econophysics forum. Avialable via DIALOG. http://www.unifr.ch/econophysics/. Accessed 1 Jul 2008

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  1. Department of Physics, University of Maryland, College Park, USA

    Victor M. Yakovenko

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  1. Victor M. Yakovenko
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Yakovenko, V.M. (2009). Econophysics, Statistical Mechanics Approach to. In: Meyers, R. (eds) Complex Systems in Finance and Econometrics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7701-4_14

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  • DOI: https://doi.org/10.1007/978-1-4419-7701-4_14

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