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

– We present generalized Green-Kubo expressions for thermal transport coefficients μ in non-conservative fluid-type systems, of the generic form μ = μ∞+ ∫ ∞ 0 dtV −1〈I exp[tL]I〉0, where exp[tL] is a pseudo-streaming operator. It consists of a sum of an instantaneous transport coefficient μ∞, and a time integral over a time correlation function in a state of thermal equilibrium between a current I and its conjugate current I . This formula with μ∞ = 0 and I = 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. The Green-Kubo formulas for thermal transport coefficients in simple classical fluids with smooth conservative interactions are widely used, and generally accepted [1–3] as exact expressions for general densities, as long as the deviations from equilibrium and the gradients are small, and the transport coefficients exist. This standard expression is given in terms of an equilibrium time correlation function between N -particle currents I and I , i.e.