Elementary Derivation of Time-Correlation Formulas for Transport Coefficients

This article presents an elementary derivation of time-correlation formulas for transport coefficients. The derivation, based on classical statistical mechanics, is modeled on one by Kubo, Yokota, and Nakajima. In agreement with theirs, it makes use of the assumption of regression of fluctuations. It differs, however, in its avoidance of Markoffian assumptions. The decisive point of the derivation is the introduction of a parameter ξ to measure the rate of the transport process. In the limit of a very slow process, i.e., in the limit ξ→0 and time t→∞ with ξt held constant, the results coincide with those obtained by Markoffian assumptions. The relation to other work, and in particular to Kirkwood's friction constant theory, is touched on briefly.