Microscopic Theory of Fluctuating Hydrodynamics in Nonlinear Lattices

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 are 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 hare transport coefficients uniquely exist for each physical system.

Automated summary

This study provides a microscopic derivation of fluctuating hydrodynamics using coarse-graining and projection techniques, highlighting the critical role of ensemble equivalence. The Green-Kubo-like formula for bare transport coefficients is presented in a computable form, showing their unique existence for each physical system within a sufficiently large but finite coarse-graining length in an infinite lattice.