Utility maximizing entropy and the second law of thermodynamics

2004/07/01 by Wojciech Słomczyński, Wojciech Slomczynski, Tomasz Zastawniak · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Economic theories and models #Stochastic processes and financial applications #math.PR #msc:37A50 #msc:49N15. #msc:60F25 #msc:91B16 #msc:94A17

paper · pdf · doi:10.1214/009117904000000117

published as Annals of Probability 2004, Vol. 32, No. 3A, 2261-2285 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000117

openalex publication_date 2004/07/01 · arxiv created 2004/10/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Expected utility maximization problems in mathematical finance lead to a generalization of the classical definition of entropy. It is demonstrated that a necessary and sufficient condition for the second law of thermodynamics to operate is that any one of the generalized entropies should tend to its minimum value of zero.

Citations

• Conjugate convex functions in optimal stochastic control

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