Stability and ensemble inequivalence in a globally coupled system

TL;DR

This paper investigates the stability of a globally coupled rotor system using a Fokker-Planck framework, revealing ensemble inequivalence and explaining quasi-stationary states observed in simulations.

Contribution

It introduces a unified Fokker-Planck approach to analyze stability differences between microcanonical and canonical ensembles in coupled rotors.

Findings

Stability varies with temperature across different solutions.

Ensemble inequivalence is demonstrated through stability analysis.

The results explain observed quasi-stationary states in numerical studies.

Abstract

We consider a system of globally coupled rotors, described by a set of Langevin equations, and examine stability of the incoherent phase. The corresponding Fokker-Planck equation, providing a unified description of microcanonical and canonical ensembles, bears a few solutions, depending upon the ensemble. It is found that the stability of each solution varies differently with the temperature, revealing the inequivalence between the two ensembles. This also suggests a physical explanation of the quasi-stationarity observed in recent numerical results.