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

Abstract

We present generalized Green-Kubo expressions for thermal transport coefficients mu in non-conservative fluid-type systems, of the generic form mu = mu(infinity)+ integral(o)(infinity) dtV(-1) [I-epsilon exp[tL] I](0), where exp[tL] is a pseudo-streaming operator. It consists of a sum of an instantaneous transport coefficient mu(infinity), 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(infinity) not equal 0 and I-epsilon not equal I covers vastly different systems, such as strongly repulsive elastic interactions in hardsphere 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.