Method of Projection in Space of Phase Space Distributions and Irreversible Processes

Abstract

This chapter differs from the others because it does not derive new results of nonequilibrium thermodynamics. It also differs in the methods it uses. Neverthe less, the contents of this chapter are closely related to the rest of the book. We consider now the question of how, from the Liouville equation, which is equivalent to the dynamic equations describing microprocesses, one can determine the irreversibility of macroprocesses, and also the Markov nature of the macroprocess in question. It is useful then to apply a projection operator defined in the space of phase space distributions. Formally, irreversibility appears as a consequence of a combination of actions of the projection operator and the time-evolution operator.