Adversarial Thermodynamics

TL;DR

The paper addresses how risk tolerance and finite sampling shape work extraction in nonequilibrium thermodynamics by introducing an adversarial resource-theoretic framework that recasts thermodynamic protocols as decision problems akin to Kelly gambling. It shows that incorporating CARA risk aversion leads to certainty equivalents expressed through Rényi divergences, connecting stochastic and resource-theoretic notions of the second law. In the finite-size regime, all Rényi divergences $D_\alpha$ gain operational meaning via a risk-reward trade-off, with optimal strategies forming an exponential family parameterized by a risk variable, and a direct correspondence $\mu = 1/(1+r)$ to expected-utility formulations. Overall, the work unifies generalized free energies with decision-theoretic principles, providing a principled, risk-aware map between nonequilibrium thermodynamics and information-theoretic gambling paradigms.

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.

Figures (1)

• Figure 1: Schematic of the adversarial Szilard engine.