Stationary properties of maximum entropy random walks

Abstract

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.

References in corpus (4)

• Dynamical criticality in the collective activity of a population of retinal neurons
• Dynamical maximum entropy approach to flocking
• A maximum entropy framework for non-exponential distributions
• Maximum caliber is a general variational principle for nonequilibrium statistical mechanics

Cited by in corpus (6)

• Maximum Caliber: a general variational principle for dynamical systems
• Entropy production rate as a criterion for inconsistency in decision theory
• Maximum Caliber Inference and the Stochastic Ising Model
• Maximum Entropy Random Walks: the Infinite Setting and the Example of Spider Networks with their Scaling Limits
• Microcanonical ensemble out of equilibrium
• Introducing user-prescribed constraints in Markov chains for nonlinear dimensionality reduction