Equilibrium fluctuations for a nongradient energy conserving stochastic model

TL;DR

This paper investigates the equilibrium energy fluctuations in a one-dimensional non-gradient stochastic model, demonstrating that the fluctuations follow a generalized Ornstein-Uhlenbeck process with a diffusion coefficient derived via an adapted non-gradient method.

Contribution

It extends the non-gradient method to a nongradient energy conserving model, deriving the diffusion coefficient and characterizing the fluctuation process.

Findings

Fluctuation process is a generalized Ornstein-Uhlenbeck process.

Diffusion coefficient is explicitly derived.

New geometric difficulties are addressed in the non-gradient method.

Abstract

In this paper we study the equilibrium energy fluctuation field of a one-dimensional reversible non gradient model. We prove that the limit fluctuation process is governed by a generalized Ornstein- Uhlenbeck process, which covariances are given in terms of the diffusion coefficient. Adapting the non gradient method introduced by Varadhan, we are able to derive the diffusion coefficient. The fact that the conserved quantity (energy) is not a linear functional of the coordinates of the system, introduces new difficulties of geometric nature when applying the nongradient method.