Abstract

A mesoscopic evolution equation for an ensemble of mesoparticles follows from the elimination of internal degrees of freedom. If the system is composed of a hierarchy of scales then the reduction procedure could be worked repeatedly and the characterization of this iterating method is carried out. Namely, a prescription describing a discrete hierarchy of master equations for the density operator is obtained. Decoherence follows from the irreversible coupling between the system, defined by mesoscopic variables, and internal degrees of freedom. We briefly discuss the existence of systems with the same dynamics laws at different scales. We made an explicit calculation for an ensemble of particles with internal harmonic interaction in an external anharmonic field. New conditions related to the semiclassical limit for mesoscopic systems (Wigner-function) are conjectured.