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

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.

18 pages, 5 figures

References in corpus (6)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Fluctuations and response of nonequilibrium states
• Path-integral analysis of fluctuation theorems for general Langevin processes
• New Green-Kubo formulas for transport coefficients in hard sphere-, Langevin fluids and the likes
• Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic and conservative interactions

Cited by in corpus (11)

• Macroscopic Stochastic Thermodynamics
• Ab initio Green-Kubo simulations of heat transport in solids: Method and implementation
• Inclusions, Boundaries and Disorder in Scalar Active Matter
• Topologically-constrained fluctuations and thermodynamics regulate nonequilibrium response
• Nonequilibrium Fluctuation-Response Relations: From Identities to Bounds
• Dissipation bounds precision of current response to kinetic perturbations
• Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks
• Fluidification of Entangled Polymers by Loop Extrusion
• Time-symmetric current and its fluctuation response relation around nonequilibrium stalling stationary state
• Thermodynamic constraints on the nonequilibrium response of one-dimensional diffusions
• Mutual Linearity is a Generic Property of Steady-State Markov Networks