  Many physicists think that the maximum entropy formalism is a straightforward
application of Bayesian statistical ideas to statistical mechanics. Some even
say that statistical mechanics is just the general Bayesian logic of inductive
inference applied to large mechanical systems. This approach identifies
thermodynamic entropy with the information-theoretic uncertainty of an (ideal)
observer's subjective distribution over a system's microstates. In this brief
note, I show that this postulate, plus the standard Bayesian procedure for
updating probabilities, implies that the entropy of a classical system is
monotonically non-increasing on the average -- the Bayesian statistical
mechanic's arrow of time points backwards. Avoiding this unphysical conclusion
requires rejecting the ordinary equations of motion, or practicing an
incoherent form of statistical inference, or rejecting the identification of
uncertainty and thermodynamic entropy.
