Game-theoretical approach to minimum entropy productions in information thermodynamics

Understand

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.