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Generalized Green-Kubo expressions for transport coefficients in fluids with impulsive, dissipative, stochastic and conservative interactions

– We present generalized Green-Kubo expressions for thermal transport coefficients μ in fluid-type systems, of the generic form, μ = μ∞ + ∫ ∞ 0 dt V −1〈Jǫ exp(tL)J〉0, i.e. 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 J and a transformed current Jǫ. The streaming operator exp(tL) generates the trajectory of a dynamical variable J(t) = exp(tL)J when used inside the thermal average 〈· · ·〉0. These formulas are valid for conservative, impulsive (hard spheres), stochastic and dissipative forces (Langevin fluids), provided the system approaches a thermal equilibrium state. In general μ∞ 6= 0 and Jǫ 6= J , except for the case of conservative forces, where the equality signs apply. We present applications for a disordered heat conductor, a Langevin fluid, and the most important one to a hard sphere fluid. The Green-Kubo formulas for thermal transport coefficients in simple classical fluids with conservative interactions are widely used, and generally accepted [1, 2, 3] as exact expressions for general densities, as long as the deviations from equilibrium and the gradients are small, and the transport coefficients exist. These expressions are given in terms of equilibrium time correlation functions between N -particle currents, i.e.