Nonequilibrium Invariant Measure under Heat Flow

TL;DR

This paper derives an explicit form of the nonequilibrium invariant measure for a harmonic oscillator chain with heat flow, revealing localized Gaussian modes with power-law tails, and extends findings to a deterministic Fermi-Pasta-Ulam chain.

Contribution

It provides a novel explicit representation of the nonequilibrium invariant measure for harmonic chains with heat flow, including a Gaussian product form and applicability to deterministic models.

Findings

Invariant measure expressed as Gaussian product with localized modes

Power-law tails observed in the measure's structure

Representation applicable to deterministic FPU chain

Abstract

We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially localized with power-law tails. Numerical studies show that such a representation applies also to a purely deterministic model, the quartic Fermi-Pasta-Ulam chain.