Information thermodynamics is what you are looking for, it's the unification of thermodynamics and information theory. Bear with me because I'm not a physicist,

Information thermodynamics is what you are looking for, it's the unification of thermodynamics and information theory. Bear with me because I'm not a physicist, but my understanding is that information needs a medium, in which way it is similar to heat, and you can use the same statistical mechanics to describe it, or fluctuation theorem, which is more precise. My understanding is that this is pretty cool stuff that solves Maxwell's demon and also sort of explains biological evolution, because apparently a system responding to it's environment is computation, performed by changing the system's state as a function of a driving signal, which results in memory about the driving signal that can be interpreted as computing a model, a model that can be predictive of the future. Now apparently how predictive that model is equals to how thermodynamically efficient the system is. Even the smallest molecular machines with memory thus must conduct predictive inference to approach maximal energetic efficiency. https://www.researchgate.net/publication/221703137_Thermodynamics_of_Prediction https://www.researchgate.net/publication/221703137_Thermodyn...