Theory of Irreversibility

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Abstract
We consider an isolated system which is exposed to external perturbations such as electric fields. The current as a linear response to a single pulse of an electric field, namely the after-effect function, is a sum of terms periodic in time in a finite system, and does not vanish after a sufficiently long time. The transfer function is defined by the Laplace transform of the aftereffect function with respect to time and thus has poles on the imaginary axis. By applying the idea of image charges in two-dimensional electrostatic problems to a certain property of the transfer function, it is shown that, in the limit of a large system, the poles on the imaginary axis are replaced by poles in the left-half plane and consequently the aftereffect function can really vanish. This fact yields the various aspects of irreversibility. It is also shown that the complex conductivity is expressed in terms of the residues of the poles of the transfer function distributed continuously on the imaginary axis, and, in particular, that the static conductivity is proportional to the residue of the pole at the origin which never exists in a finite system but appears in an infinite system. General reciprocal relations are given for both irreversible and reversible thermodynamics, and their connection to Onsager's and Maxwell's relations are discussed. An expression for the entropy production is given and a new interpretation of the H-function is proposed.