Classical analogue of the statistical operator

We advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system. Fil: Plastino, Ángel Luis. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Granada. Facultad de Ciencias. Departamento de Electromagnetismo y Física de la Materia. Instituto "Carlos I" de Física Teórica y Computacional; España