Kramers and non-Kramers Phase Transitions in Many-Particle Systems with Dynamical Constraint

TL;DR

This paper investigates phase transitions in many-particle systems governed by a Fokker-Planck equation with a double-well potential, focusing on the effects of nonlocal dynamical constraints and multiple small parameters.

Contribution

It introduces reduced dynamical models for various phase transition regimes in systems with nonlocal constraints, expanding understanding of Kramers and non-Kramers transitions.

Findings

Identification of multiple parameter regimes affecting phase transitions

Derivation of reduced models capturing system dynamics

Insights into the role of nonlocal constraints in phase behavior

Abstract

We study a Fokker-Planck equation with double-well potential that is nonlocally driven by a dynamical constraint and involves two small parameters. Relying on formal asymptotics we identify several parameter regimes and derive reduced dynamical models for different types of phase transitions.