A MICROSCOPIC PERSPECTIVE ON THE PHYSICAL FOUNDATIONS OF CONTINUUM-MECHANICS .2. A PROJECTION OPERATOR APPROACH TO THE SEPARATION OF REVERSIBLE AND IRREVERSIBLE CONTRIBUTIONS TO MACROSCOPIC BEHAVIOR

Reproducible macroscopic behaviour (at some pair of length-time scales ), for a confined material system with passive environment, is analyse d in terms of a projection operator P on the space of functions f of m icroscopic state. When f represents a local (macroscopic) spatial aver age, assumptions of local equilibrium and dynamic ergodicity establish Pf as the corresponding reproducible space-time average. Time evoluti on of the macroscopic probability density, induced by the microscopic probability density associated with partial initial information, is sh own to equal the sum of explicit time-reversible and time-irreversible contributions via an analysis involving g-function formalism and oper ators defined in terms of P, its complementary projection. and the Lio uville operator. An indication is given of how this evolution equation (the master equation) yields the relevant Fokker-Planck and Langevin equations (continuum equations of balance in which fields have stochas tic attributes) to be treated in Part III. (C) 1997 Elsevier Science L td.