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Maximum caliber inference and the stochastic Ising model.

Carlo Cafaro1, Sean Alan Ali2

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We introduce a novel inference algorithm for predicting complex system dynamics using maximum caliber. This method, applied to nonequilibrium systems, formally connects to the Glauber rule at high temperatures.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Theoretical Physics

Background:

  • Complex nonequilibrium stationary systems often lack complete information.
  • Predicting their dynamical properties requires robust inference algorithms.

Purpose of the Study:

  • To investigate the maximum caliber variational principle as an inference algorithm.
  • To predict dynamical properties of complex nonequilibrium stationary systems with incomplete information.

Main Methods:

  • Maximizing path entropy over discrete time step trajectories.
  • Applying normalization, stationarity, and detailed balance constraints.
  • Incorporating a path-dependent dynamical information constraint.

Main Results:

  • A general expression for transition probabilities of stationary Markov processes was computed.
  • A perturbative asymptotic expansion was performed.
  • Formal overlap with the Glauber rule for the stochastic Ising model was found at high temperatures.

Conclusions:

  • The maximum caliber principle provides a framework for inferring dynamics in complex systems.
  • The method offers a theoretical link between general principles and specific models like the Ising model.