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

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.