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A thermodynamic-like approach for the study of probabilistic systems

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  • Campos, Diógenes

Abstract

This paper starts by considering an arbitrary system for which the probability distribution P:={P1,P2,…,PN} of a measurable property, with N possible independent results, is known. By using the Hartley information (pseudo-energy), the escort probabilities of P and its Shannon entropy, a thermodynamic-like formalism is developed, including the deduction of the fundamental equation for the mean value of the pseudo-energies. Thus, the method allows a macrodescription of the system that is based on a purely mathematical procedure and involves thermodynamic-like variables. As a specific example we consider a bank that measures customer satisfaction by doing a statistical survey (satisfied or unsatisfied customers).

Suggested Citation

  • Campos, Diógenes, 2011. "A thermodynamic-like approach for the study of probabilistic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 214-222.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:2:p:214-222
    DOI: 10.1016/j.physa.2010.09.023
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    1. Stephen Morris & Hyun Song Shin, 2001. "Rethinking Multiple Equilibria in Macroeconomic Modeling," NBER Chapters, in: NBER Macroeconomics Annual 2000, Volume 15, pages 139-182, National Bureau of Economic Research, Inc.
    2. Campos, Diógenes, 2010. "Real and spurious contributions for the Shannon, Rényi and Tsallis entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3761-3768.
    3. Beck, Christian, 2004. "Superstatistics, escort distributions, and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 139-144.
    4. Campos, Diógenes, 2010. "Rényi and Tsallis entropies for incomplete or overcomplete systems of events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 981-992.
    5. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
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    Cited by:

    1. Campos, Diógenes, 2014. "Macroscopic characterization of data sets by using the average absolute deviation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 222-234.
    2. Campos, Diógenes, 2012. "On a modified quantum statistical mechanics based on the Hartley information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5439-5452.
    3. Campos, Diógenes, 2011. "A thermodynamic-like characterization of Colombia’s presidential elections in 2010, and a comparison with other Latin American countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1779-1790.

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