An Explicit Microreversibility Violating Thermodynamic Markov Process

TL;DR

This paper constructs a non-microreversible Markov process and demonstrates that thermodynamic Monte Carlo algorithms do not strictly require microreversibility, challenging traditional assumptions in statistical physics.

Contribution

It introduces a explicit non-microreversible transition matrix and applies it to the three-state Potts model, showing microreversibility is not essential.

Findings

Non-microreversible transition matrix constructed

Applied to three-state Potts model

Microreversibility not strictly necessary for thermodynamic algorithms

Abstract

We explicitly construct a non-microreversible transition matrix for a Markov process and apply it to the standard three-state Potts model. This provides a clear and simple demonstration that the usual micoreversibility property of thermodynamical Monte Carlo algorithms is not strictly necessary from a mathemetical point of view.