Method of Natural Projector

Abstract

P. and T. Ehrenfest introdused in 1911 a model of dynamics with a coarse-graining of the original conservative system in order to introduce irreversibility [15]. Ehrenfests considered a partition of the phase space into small cells, and they have suggested to combine the motions of the phase space ensemble due to the reversible dynamics with the coarse-graining (“shaking”) steps - averaging of the density of the ensemble over the phase cells. This generalizes to the following: alternations of the motion of the phase ensemble due to the microscopic equations with returns to the quasiequilibrium manifold while preserving the values of the macroscopic variables. We here develop a formalism of nonequilibrium thermodynamics based on this generalization. The Ehrenfests’ coarse-graining can be treated as a a result of interaction of the system with a generalized thermostat. There are many ways for introduction of thermostat in computational statistical physics [283], but the Ehrenfests’ approach remains the basic for understanding the irreversibility phenomenon.