Maximum Caliber Inference and the Stochastic Ising Model

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.

21 pages, no figures

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Cited by in corpus (10)

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• Theoretical investigations of an information geometric approach to complexity
• Theoretical analysis of a nearly optimal analog quantum search
• Comment on "Black Hole Entropy: A Closer Look"
• Transition Probabilities in Generalized Quantum Search Hamiltonian Evolutions
• Information Geometric Complexity of Entropic Motion on Curved Statistical Manifolds under Different Metrizations of Probability Spaces
• Information Geometric Aspects of Probability Paths with Minimum Entropy Production for Quantum State Evolution
• An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information