Nonequilibrium Green-Kubo relations for hydrodynamic transport from an equilibrium-like fluctuation-response equality

TL;DR

This paper extends Green-Kubo relations to certain far-from-equilibrium steady states, linking response and fluctuations through an equilibrium-like fluctuation-response equality, and validates these relations in specific model systems.

Contribution

It introduces a class of perturbations that relate response to steady-state correlations far from equilibrium, deriving nonequilibrium Green-Kubo relations for hydrodynamic transport coefficients.

Findings

Derived nonequilibrium Green-Kubo relations for hydrodynamic variables.

Validated predictions through analytical and numerical studies.

Provided a theoretical basis for Onsager's regression hypothesis near nonequilibrium.

Abstract

Near equilibrium, Green-Kubo relations provide microscopic expressions for macroscopic transport coefficients in terms of equilibrium correlation functions. At their core, they are based on the intimate relationship between response and fluctuations as embodied by the equilibrium fluctuation-dissipation theorem, a connection generically broken far from equilibrium. In this work, we identify a class of perturbations whose response around far-from-equilibrium steady states is linked to steady-state correlation functions via an equilibrium-like fluctuation-response equality. We then utilize this prediction to substantiate linearized hydrodynamic transport equations that describe how spatial inhomogeneities in macroscopic nonequilibrium systems relax. As a consequence, we derive nonequilibrium Green-Kubo relations for the transport coefficients of two types of hydrodynamic variables: local conserved densities and broken-symmetry modes. A byproduct of this work is to provide a theoretical foundation for the validity of Onsager's regression hypothesis around nonequilibrium steady states. Our predictions are analytically and numerically corroborated for two model systems: density diffusion in a fluid of soft, spherical active Brownian particles and phase diffusion in the noisy Kuramoto model on a square lattice.