Great paper! There are some similar ideas to this in game theory and reinforcement learning (RL):

[1]: Thermodynamic Game Theory: https://adamilab.msu.edu/wp-content/uploads/AdamiHintze2018....

[2]: piKL - KL-regularized RL: https://arxiv.org/abs/2112.07544

[3]: Soft-Actor Critic - Entropy-regularized RL: https://arxiv.org/abs/1801.01290

[4]: "Soft" (Boltzmann) Q-learning = Entropy-regularized policy gradients: https://arxiv.org/abs/1704.06440