Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures

TL;DR

This paper develops a stochastic approach to model finite-N effects in mean-field systems, deriving a Fokker-Planck equation to analyze the decay of coherent structures and estimate their lifetimes.

Contribution

It introduces a stochastic framework that captures finite-N effects in mean-field systems and provides analytical tools to estimate the lifetime of coherent structures.

Findings

Derived a general Fokker-Planck equation for finite-N effects.

Analytically computed the decay of coherent structures.

Estimated thermalization timescales in mean-field systems.

Abstract

A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably the disintegration of coherent structures that may sustain out-of-equilibrium quasistationary states. The time evolution of the fraction of particles remaining close to a mean-field potential trough is analytically computed. This indicator enables to estimate the lifetime of coherent structures and thermalization timescale in mean-field systems.