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

TL;DR

This paper bridges stochastic thermodynamics and expected utility theory, providing new interpretations of divergence measures as certainty equivalents of dissipated work and extending fundamental thermodynamic relations.

Contribution

It introduces a novel connection between Renyi divergences and utility-based interpretations of entropy production in thermodynamics.

Findings

Renyi divergence as certainty equivalent for dissipated work

New interpretation of extreme risk aversion and risk-seeking in thermodynamics

Generalized Jarzynski equality and broader divergence class

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 $\alpha$ R\'enyi 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.