Fisher and Jaynesian statistics compared in the description of classical fluids

Abstract

Fisher statistics provides an information measure which, like that of Shannon, is a functional of a distribution f. The latter solves an Euler equation to minimize the functional. To make comparison with statistical derivations of extended thermodynamics, calculations by Frieden, Plastino, and collaborators are specialized to the case where f is a phase-space distribution approximating a solution of the Liouville equation. The Euler equations are solved subject to conditions specifying values of internal energy and fluxes, e.g. of heat and momentum. The solution is compared with that of Jaynes which, with information theory, provides an entropy model. The Fisher and Jaynes entropies are identical only in equilibrium. The distributions agree in linear approximation for a restricted set of variables. This set is large enough to embrace all those needed in the classical non-equilibrium description of simple fluids. Fisher-Euler solutions are not unique in non-equilibrium.