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.
Highlights
The fluctuation-dissipation theorem (FDT) is a cornerstone of statistical mechanics [1,2,3,4]
A major consequence has been in refining our understanding of the material coefficients that determine how spatial inhomogeneities in near-equilibrium macroscopic systems relax via hydrodynamic transport
II, we identified a class of dynamical perturbations whose response can be identified as a simple correlation function, akin to the equilibrium FDT
Summary
The fluctuation-dissipation theorem (FDT) is a cornerstone of statistical mechanics [1,2,3,4]. The resulting predictions, known as Green-Kubo relations, equate these macroscopic transport coefficients D to the microscopic equilibrium correlation functions of local current observables jr(t ), whose fluctuations depend on space r and time t in a volume V [4,5,6,7,8,9,10], Dχ = β V. The resulting Green-Kubo relations incorporate a time-reversed dynamics, apparently obscuring the interpretation of the resulting correlation functions This obstacle has been overcome for at least one specific model of a nonequilibrium active fluid [30]. This observation generalizes our previous work on the static response to time-dependent perturbations [31] We exploit this equilibrium-like fluctuation-response equality to provide a theoretical foundation for linearized hydrodynamic equations governing transport in homogeneous nonequilibrium fluids. Our theory is illustrated by numerical simulations of two examples, a fluid of soft active Brownian particles and a noisy Kuramoto model
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