Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices

TL;DR

This paper provides a microscopic derivation of fluctuating hydrodynamics in nonlinear lattices, clarifying the role of coarse-graining and ensemble equivalence, and demonstrating the existence of transport coefficients through numerical simulations.

Contribution

It offers the first microscopic derivation of fluctuating hydrodynamics in nonlinear lattices using coarse-graining and projection techniques.

Findings

Bare transport coefficients exist for large enough coarse-graining lengths.

The Green-Kubo like formula is numerically computable.

Transport coefficients are unique for each physical system.

Abstract

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK) like formula for the bare transport coefficients is presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system.