On some properties of the Mandel-Turner equation

Abstract

As shown recently by the Brussels group, an unified formulation of statistical mechanics and thermodynamics can be obtained. This requires the introduction of starunitary transformations A(L). One of the operators (x) necessary to construct explicitly such transformations satisfies the Mandel-Turner equation. The aim of this paper is to investigate some properties of this equation. First we show that, for a large class of systems, x is even with respect to the inversion L → — L, L being the Liouville-von Neumann operator. Next, we solve explicitly the Mandel-Turner equation for the Friedrichs' model.