Game-theoretical approach to minimum entropy productions in information thermodynamics

TL;DR

This paper applies game theory to optimize entropy production in interconnected thermodynamic subsystems, revealing trade-offs and strategies for minimizing total entropy in biological and physical systems.

Contribution

It introduces a game-theoretic framework for minimizing entropy production in coupled subsystems within linear irreversible thermodynamics, including Nash equilibrium solutions.

Findings

Trade-off between partial entropy productions of subsystems.

Total entropy production minimized when penalties are equally shared.

Possible biological relevance to E. coli chemotaxis.

Abstract

In a situation where each player has control over the transition probabilities of each subsystem, we game-theoretically analyze the optimization problem of minimizing both the partial entropy production of each subsystem and a penalty for failing to achieve a given state transition. In the regime of linear irreversible thermodynamics, we obtain the Nash equilibrium solution of the probability flow and calculate each partial entropy production for this solution. We find a trade-off such that a partial entropy production should be larger if we want the other partial entropy production to be smaller. The total entropy production can be minimized if each subsystem equally shares the penalty. We identify that this trade-off is due to the interacting contribution of the probability flow and discuss a possible biological validity for Escherichia coli chemotaxis.