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.
Institute for Theoretical Physics, Universiteit Utrecht, 3508 TD Utrecht, The Netherlands.
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Ernst
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Brito