Maximum Caliber Inference and the Stochastic Ising Model

TL;DR

This paper applies the maximum caliber principle to infer transition probabilities in nonequilibrium stochastic systems, revealing a connection to the Glauber dynamics of the Ising model at high temperatures.

Contribution

It derives a general expression for transition probabilities in nonequilibrium stationary systems using maximum caliber, linking it to the Glauber rule in the high-temperature limit.

Findings

Derived a general transition probability expression for nonequilibrium systems.

Showed the connection between maximum caliber inference and Glauber dynamics.

Identified conditions under which the stochastic Ising model emerges from maximum caliber.

Abstract

We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.