Statistical Mechanics of Reinforcement Learning

Hello, fellow learners! Are there established connections between certain RL algorithms and certain physical systems? For example, the Hopfield network (a type of recurrent neural network) is related to spin glasses in condensed matter physics.

Are there similar types of connections for traditional RL algorithms such as Q-learning, SARSA, TD(lamdbda), etc? I have heard that the Hamilton-Jacobi equation in classical mechanics is a special case of the Hamilton-Jacobi-Bellman equation, but I’m curious about other connections.

I’m primarily asking about non-deep RL since neural networks already have connections to statistical mechanics and condensed matter physics, but I’m open to learning whatever insights you all might have.