New Green-Kubo formulas for transport coefficients in hard sphere-, Langevin fluids and the likes

TL;DR

This paper introduces generalized Green-Kubo formulas for thermal transport coefficients applicable to various non-conservative fluid systems, unifying different interaction types and extending traditional formulas.

Contribution

The authors derive a unified Green-Kubo expression for transport coefficients in non-conservative fluids, encompassing systems with elastic, dissipative, and stochastic interactions.

Findings

Derived generalized Green-Kubo formulas for diverse systems

Reduced to standard formulas for conservative systems

Applicable to hard sphere and Langevin fluids

Abstract

We present generalized Green-Kubo expressions for thermal transport coefficients $\mu$ in non-conservative fluid-type systems, of the generic form, $\mu$ $= \mu_\infty$ $+\int^\infty_0 dt V^{-1} \av{I_\epsilon \exp(t {\cal L}) I}_0$ where $\exp(t{\cal L})$ is a pseudo-streaming operator. It consists of a sum of an instantaneous transport coefficient $\mu_\infty$, and a time integral over a time correlation function in a state of thermal equilibrium between a current $I$ and its conjugate current $I_\epsilon$. This formula with $\mu_\infty \neq 0$ and $I_\epsilon \neq I$ covers vastly different systems, such as strongly repulsive elastic interactions in hard sphere fluids, weakly interacting Langevin fluids with dissipative and stochastic interactions satisfying detailed balance conditions, and "the likes", defined in the text. For conservative systems the results reduce to the standard formulas.