Application of Thermodynamics Entropy Concept in Financial Markets

  • Sellamuthu Prabakaran
Conference paper
Part of the Springer Proceedings in Business and Economics book series (SPBE)


Entropy is a mathematically defined quantity that is generally used for characterizing the probability of outcomes in a system that is undergoing a process. It was originally introduced in thermodynamics by Rudolf Clausius (Philos Mag J Sci 40:122–127, 1870) to measure the ratio of transferred heat through a reversible process in an isolated system. In statistical mechanics the interpretation of entropy is the measure of uncertainty about the system that remains after observing its macroscopic properties (pressure, temperature, or volume). In this work, we attempt that the concept of entropy in thermodynamics be applied to financial markets. The main goal of this study is fourfold: (1) First we begin our approach through the concept of financial economics entropy. (2) Next we introduce the concept of entropy in economic systems. (3) Here we are exploring the interpretation of entropy in finance. (4) Then we extend the concept of entropy used in finance with standard economic utility theory by using of entropy and its maximization. (5) Finally, we construct the model of variance equilibrium under an entropy (financial) risk measure. And this paper ends with conclusion.


Financial markets Entropy Shannon entropy Risk measure and thermodynamics 


  1. Aoki, M. (2002). Modeling aggregate behavior and fluctuations in economics: Stochastic views of interacting agents. Cambridge: Cambridge University Press.Google Scholar
  2. Beaudreau, B. (1998). Energy and organization: Growth and distribution reexamined. Westport, CT: Greenwood Press.Google Scholar
  3. Beirlant, J., Dudewicz, E. J., Györfi, L., & Van der Meulen, E. C. (1997). Nonparametric entropy estimation: An overview. International Journal of Mathematical and Statistical Sciences, 6, 17–40.Google Scholar
  4. Biddle, J. (2001). Economics broadly considered: Essays in honor of Warren J. Samuels. New York: Routledge.CrossRefGoogle Scholar
  5. Blake, D. (2000). Financial market analysis. Chichester: Wiley.Google Scholar
  6. Board, J. (2002). Transparency and fragmentation: Financial market regulation in a dynamic environment. New York: Palgrave.CrossRefGoogle Scholar
  7. Boltzmann, L., & Hasenöhrl, F. (2012). Weitere Studien u¨ber das Wa¨rmegleichgewicht unter Gas-moleku¨ len Wissenschaftliche Abhandlungen. Cambridge University Press. doi:
  8. Çengel, Y. A., & Boles, M. A. (2011). “6–7.” Thermodynamics: An engineering approach (7thed., p. 299). New York: McGraw-Hill. Print.Google Scholar
  9. Claesens, S. (2006). A reader in international corporate finance (Vol. 2). Washington, DC: World Bank.Google Scholar
  10. Clausius, R. (1870). XVI. On a mechanical theorem applicable to heat. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 40, 122–127. CrossRefGoogle Scholar
  11. Cleveland, C. (2006). Dictionary of Energy, Amsterdam: Elsevier. Wissler, J. (2006). Achieving balance. Air and Space Power Journal, 23(4), 25–35.Google Scholar
  12. Das, D. (2003). International finance: Contemporary issues. New York: Routledge.Google Scholar
  13. Dincer, I. (2007). Exergy: Energy, environment, and sustainable development. Boston: Elsevier.Google Scholar
  14. Dionisio, A., Menezes, R., & Mendes, D. A. (2006). An econophysics approach to analyse uncertainty in financial markets: An application to the Portuguese stock market. The European Physical Journal B, 50, 161–164. Scholar
  15. El-Sayed, M. (2003). The thermoeconomics of energy conversions. Oxford: Pergamon.Google Scholar
  16. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman lectures on physics. Addison-Wesley Publishing Company.Google Scholar
  17. Freedman, D., & Diaconis, P. (1981). On the histogram as a density estimator: L2 theory. Probability Theory and Related Fields, 57, 453–476. Scholar
  18. Giordano, N. (2009). College physics: Reasoning and relationships (p. 510). Cengage Learning. 0-534-42471-6.Google Scholar
  19. Halliday, D., & Resnick, R. (1978). Physics (3rd ed.). John Wiley & Sons.Google Scholar
  20. Hansen, A. (1953). A guide to Keynes. New York: McGraw Hill.Google Scholar
  21. Härdle, W. (2004). Nonparametric and semiparametric models. Springer. doi: Scholar
  22. Hartley, R. V. L. (1928). Transmission of information. Bell System Technical Journal, Blackwell Publishing Ltd, 7(3), 535–563.CrossRefGoogle Scholar
  23. Kirchner, U., & Zunckel, C. (2011). Measuring Portfolio diversification. arXiv preprint arXiv:11024722.Google Scholar
  24. Kittel, C., & Kroemer, H. (1980). Thermal physics (2nd ed.). W. H. Freeman Company.Google Scholar
  25. Kostic, M. (2011). “Revisiting The Second Law of Energy Degradation and Entropy Generation: From Sadi Carnot's Ingenious Reasoning to Holistic Generalization”. AIP Conf. Proc. American Institute of Physics.Google Scholar
  26. Maasoumi, E., & Racine, J. (2002). Entropy and predictability of stock market returns. Journal of Econometrics, 107, 291–312. doi: Scholar
  27. Malkiel, B. G. (2007). Random walk down wall street: The time-tested strategy for successful investing. Mishawaka, IN: Better World Books.Google Scholar
  28. Mensi, W., et al. (2012). Crude oil market efficiency: An empirical investigation via the shannon entropy. International Economics, 129, 119–137.CrossRefGoogle Scholar
  29. Molgedey, L., & Ebeling, W. (2000). Local order, entropy and predictability of financial time series. The European Physical Journal B-Condensed Matter and Complex Systems, 15(4), 733–737.CrossRefGoogle Scholar
  30. Nawrocki, D. N., & Harding, W. H. (1986). State-value weighted entropy as a measure of investment risk. Applied Economics, 18, 411–419. Scholar
  31. von Neumann, J. (1947). Theory of games and economic behavior, Princeton University Press, Second Printing.Google Scholar
  32. Nyquist, H. (1924). Certain factors affecting telegraph speed. Bell System Technical Journal, Blackwell Publishing Ltd, 3(2), 324–346.CrossRefGoogle Scholar
  33. Nyquist, H. (1928). Certain topics in telegraph transmission theory. Transactions of the American Institute of Electrical Engineers, 47(2), 617–644.CrossRefGoogle Scholar
  34. Petroni, F., & Serva, M. (2003). Spot foreign exchange market and time series. The European Physical Journal B - Condensed Matter and Complex Systems, 34(4), 495–500.CrossRefGoogle Scholar
  35. Philippatos, G. C., & Wilson, C. J. (1972). Entropy, market risk, and the selection of efficient portfolios. Applied Economics, 4, 209–220. Scholar
  36. Renyi, A. (1961). On measures of entropy and information. Fourth Berkeley symposium on Mathematical statistics and probability (pp. 547–561). Berkeley, CA: University of California Press.Google Scholar
  37. Scott, D. W. (1979). On optimal and data-based histograms. Biometrika, 66, 605–610. Scholar
  38. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423. Scholar
  39. Shannon, C. E. (2001). A mathematical theory of communication. SIGMOBILE Mob. Comput. Commun. Rev., ACM, New York, NY, USA, 5(1), 3–55.CrossRefGoogle Scholar
  40. Silverman, B. W. (1986). Density estimation for statistics and data analysis. CRC press. Monographs on Statistics and Applied Probability, p. 26. doi:
  41. Turlach, B. A. (1993). Bandwidth selection in kernel density estimation: A review: Universite´ catholique de Louvain. doi: Scholar
  42. Wachowiak, M. P., Smolikova, R., Tourassi, G. D., & Elmaghraby, A. S. (2005). Estimation of generalized entropies with sample spacing. Pattern Analysis and Applications, 8, 95–101. Scholar
  43. Yang, J. S., Kwak, W., & Kaizoji, T. (2008). Increasing market efficiency in the stock markets. The European Physical Journal B, 61(2), 241–246.CrossRefGoogle Scholar
  44. Zapart, C. A. (2009). On entropy, financial markets and minority games. Physica A: Statistical Mechanics and its Applications, 388(7), 1157–1172.CrossRefGoogle Scholar
  45. Zhang, Y.-C. (1999). Toward a theory of marginally efficient markets. Physica A: Statistical Mechanics and its Applications, 269(1), 30–44.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economics and Business Administration, Department of Accounting & FinancePontificia Universidad Javeriana CaliCaliColombia

Personalised recommendations