Entropy Production in Classical and Quantum Systems

#### C.-A. Pillet

2001, v.7, Issue 1, 145-157

ABSTRACT

Koopmanism - the spectral theory of dynamical systems - reduces the study of dynamical properties of a classical or quantum system S to the spectral analysis of its Liouvillean $L_S$. By definition, the operator $L_S$ implements the dynamics on a suitable representation of the observable algebra of S. Near thermal equilibrium, this representation can often be constructed explicitly. Recent developments have shown that, in this situation, spectral analysis becomes a powerful tool in the study of thermal relaxation processes. Far from thermal equilibrium, the explicit construction of stationary states and of the corresponding representations is usually not possible. Nevertheless, important physical properties of the system S can be obtained from a fairly simple mathematical analysis. In this work, I investigate entropy production in open systems driven away from equilibrium by thermodynamic forces.

Keywords: nonequilibrium statistical mechanics,open systems,Hamiltoniansystems,entropy production,Koopmanism