Theory of Thermal Transport Coefficients

A simple proof of the usual correlation-function expressions for the thermal transport coefficients in a resistive medium is given. This proof only requires the assumption that the phenomenological equations in the usual form exist. It is a mechanical derivation in the same sense that Kubo's derivation of the expression for the electrical conductivity is. That is, a purely Hamiltonian formalism with external fields is used, and one never has to make any statements about the nature or existence of a local equilibrium distribution function, or how fluctuations regress. For completeness the analogous formulas for the viscosity coefficients and the heat conductivity of a simple fluid are given.