The Annals of Probability

Utility maximizing entropy and the second law of thermodynamics

Wojciech Słomczyński and Tomasz Zastawniak

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 32, Number 3 (2004), 2261-2285.

Dates
First available in Project Euclid: 14 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1089808425

Digital Object Identifier
doi:10.1214/009117904000000117

Mathematical Reviews number (MathSciNet)
MR2073191

Zentralblatt MATH identifier
1047.60101

Subjects
Primary: 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]
Secondary: 94A17: Measures of information, entropy 60F25: $L^p$-limit theorems 91B16: Utility theory 49N15: Duality theory

Keywords
Entropy Markov operators utility maximization exactness H-theorem second law of thermodynamics

Citation

Słomczyński, Wojciech; Zastawniak, Tomasz. Utility maximizing entropy and the second law of thermodynamics. Ann. Probab. 32 (2004), no. 3, 2261--2285. doi:10.1214/009117904000000117. https://projecteuclid.org/euclid.aop/1089808425


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