Adversarial Thermodynamics

Abstract

In thermodynamics, an agent's ability to extract work is fundamentally constrained by their environment. Traditional frameworks struggle to capture how strategic decision-making under uncertainty, particularly an agent's tolerance for risk, determines the trade-off between extractable work and probability of success in finite-scale experiments. Here, we develop a framework for nonequilibrium thermodynamics based on adversarial resource theories, in which work extraction is modeled as an adversarial game for an agent extracting work. Within this perspective, we consider a Szilard-type engine as a game isomorphic to Kelly gambling, an information-theoretic model of optimal betting under uncertainty -- but with a thermodynamic utility function. Extending the framework to finite-size regimes, we apply a risk-reward trade-off to find an interpretation of the Renyi divergences in terms of extractable work for a given failure probability. By incorporating risk sensitivity via utility functions, we show that the guaranteed amount of work a rational agent would accept instead of undertaking a risky protocol is given by a Renyi divergence. This provides a unified picture of thermodynamics and gambling, and highlights how generalized free energies emerge from an adversarial setup.