[srean]

In Boltzmann's formulation of stat-mech it comes from the assumption that when a system is in "equilibrium", then all the micro-states that are consistent with the macro-state are equally occupied. That's the basis of the theory. A prime mover is thermal agitation.

It can be circular if one defines equilibrium to be that situation when all the micro-states are equally occupied. One way out is to define equilibrium in temporal terms - when the macro-states are not changing with time.

[mitthrowaway2]

The Bayesian reframing of that would be that when all you have measured is the macrostate, and you have no further information by which to assign a higher probability to any compatible microstate than any other, you follow the principle of indifference and assign a uniform distribution.

[srean]

Yes indeed, thanks for pointing this out. There are strong relationships between max-ent and Bayesian formulations.

For example one can use a non-uniform prior over the micro-states. If that prior happens to be in the Darmois-Koopman family that implicitly means that there are some non explicitly stated constraints that bind the micro-state statistics.