On the construction of the microscopic entropy operator in the non-canonical formalism

Abstract

In the formulation of a microscopic theory of irreversible processes as proposed by the Brussels group, a bilinear functional of the density operator in the physical representation serves as a Liapounov function, and therefore as a microscopic model for entropy. The construction of this functional is explicitely indicated in the frame of a perturbative approach. Some care has to be taken as each order in the perturbation expansion contains divergent terms. It is however shown that a resummation of divergent terms of various orders leads to a well-behaved expression. The divergence has an interesting meaning : it indicates that the microscopic entropy cannot be obtained by expansion in a coupling parameter or concentration. This breakdown of the perturbative approach is also related to the inadequacy of the Boltzmann-like behaviour, as examplified by the "long tails" observed in computer simulation.