Maxwell's Demon Walks into Wall Street: Stochastic Thermodynamics Meets Expected Utility Theory

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's fluctuation relations, every alpha Re ' nyi 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 = infinity are recovered and receive the new interpretation of being associated with 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.