Fluctuation Form of Transport Theory

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Abstract
Einstein-type expressions for transport coefficients are obtained by introducing Onsager's regression hypothesis for fluctuations into the statistical-mechanical expressions for the fluxes. Liouville operator formalism is used to convert the fluxes into a general fluctuation form. Introduction of a local equilibrium distribution function and linearization in the macroscopic gradients yield the Einstein-type equations. An extension of the results to interference effects is given. The fluctuation form of the fluxes is converted into one in which the nonequilibrium distribution function is used. The latter expressions form the basis for the theories of Kirkwood, Rice and Allnatt, and others. An application is made to particles interacting via a square-well potential.