You might be trying to be too literal. What makes statistical mechanics so brilliant is that it takes first principle ideas (particle energies + ensemble) to d

You might be trying to be too literal. What makes statistical mechanics so brilliant is that it takes first principle ideas (particle energies + ensemble) to derive macroscopic thermodynamic rules, all of which were originally derived from observation. What the OP is proposing is a mathematical analysis of SGD + generic deep learning architectures might be able to derive the rules we have empirically derived from experiments in model training.