Thermodynamics with benefit of Jaynes distinction
Physics describes the dice (e.g. multiplicities);
Gambling theory figures the best guess.
Applies to any system about which we have only partial knowledge.
Entropy is simply the logarithm of multiplicity, in bits or nats.
Zeroth Law is a quantitative theorem about uncertainty slopes (dS/dX) for any conserved randomly-shared quantity X!
Reciprocal temperature is the uncertainty slope dS/dE with physical units such that Troom=1/40 eV/nat.
Equipartition, equations of state, laws of mass action, and even fluctuations, all follow simply from multiplicities.
Predicted heat flows are simply one’s best bet.