Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic, and conservative interactions.

We present a generalization of the Green-Kubo expressions for thermal transport coefficients mu in complex fluids of the generic form [equation see text], i.e., a sum of an instantaneous transport coefficient muinfinity, and a time integral over a time correlation function in a state of thermal equilibrium between a current J and its conjugate current Jepsilon. 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 muinfinity not equal 0 and Jepsilon not equal J, except for the case of conservative forces, where the equality signs apply. The most important application in the present paper is the hard sphere fluid.