Maximum entropy estimation of transition probabilities of reversible Markov chains

TL;DR

This paper develops a maximum entropy framework for estimating transition probabilities in reversible Markov chains, applicable to various physical models including classical spin systems like Ising, Potts, and Blume-Emery-Griffiths models.

Contribution

It introduces a general theoretical approach for transition probability estimation in reversible Markov chains using maximum entropy, with applications to classical spin models.

Findings

Unified maximum entropy estimation method for reversible Markov chains

Application to classical spin models demonstrating the approach

Potential for broad physical system modeling

Abstract

In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use one-dimensional classical spin systems to illustrate the theoretical ideas. The examples studied in this paper are: the Ising model, the Potts model and the Blume-Emery-Griffiths model.