  Maximum entropy (maxEnt) inference of state probabilities using
state-dependent constraints is popular in the study of complex systems. In
stochastic dynamical systems, the effect of state space topology and
path-dependent constraints on the inferred state probabilities is unknown. To
that end, we derive the transition probabilities and the stationary
distribution of a maximum {\it path} entropy Markov process subject to state-
and path-dependent constraints. The stationary distribution reflects a
competition between path multiplicity and imposed constraints and is
significantly different from the Boltzmann distribution. We illustrate our
results with a particle diffusing on an energy landscape. Connections with the
path integral approach to diffusion are discussed.
