Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory

Abstract

The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks' fluctuation relations, every $\alpha$ Rényi divergence between the forward process and its reverse has the operational meaning of the ``certainty equivalent'' of dissipated work (or, more generally, of entropy production) for a player with risk aversion $r=\alpha -1$. The two known cases $\alpha =1$ and $\alpha =\infty$ are recovered and receive the new interpretation of being associated to a risk-neutral and an extreme risk-averse player respectively. Among the new results, the condition for $\alpha =0$ describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences.

5 pages, 1 figure

References in corpus (3)

• Dissipation: The phase-space perspective
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Thermodynamics of exponential Kolmogorov-Nagumo averages

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