Fundamentally, thermodynamics and information theory share a slew of similar ideas. Because in a lot of ways information theory came out of a thermodynamic thought process applied to signals. Even more recent work in ml like Boltzmann machines are directly taken from this overlap. That being said stronger theoretical connections are well worth the effort as these fields do have some different ideas that if shown to be similar can yield discoveries and push our understanding forward. Some thoughts that come to mind are compression, model generalizability/ convergence.