title: Stationary properties of maximum-entropy random walks.
abstract: Maximum-entropy (ME) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic systems, how state space topology and path-dependent constraints affect ME-inferred state probabilities remains unknown. To that end, we derive the transition probabilities and the stationary distribution of a maximum path entropy Markov process subject to state- and path-dependent constraints. A main finding is that the stationary distribution over states differs significantly from the Boltzmann distribution and reflects a competition between path multiplicity and imposed constraints. We illustrate our results with particle diffusion on a two-dimensional landscape. Connections with the path integral approach to diffusion are discussed.
authors.affiliation: Department of Systems Biology, Columbia University, New York, New York 10032, United States.
authors.forename: Purushottam D
authors.initials: PD
authors.lastname: Dixit
mesh_terms: D004058:Diffusion; D019277:Entropy; D008390:Markov Chains; D008962:Models, Theoretical