The Annals of Probability

Utility maximizing entropy and the second law of thermodynamics

Wojciech Słomczyński and Tomasz Zastawniak

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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

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

First available in Project Euclid: 14 July 2004

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Zentralblatt MATH identifier

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

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


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.

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