Projection Operator Techniques in Nonequilibrium Statistical Mechanics

Ever since the time of tomate, the desire to understand how sacrecabic tr sible behavior arises out of the complexity of the underlying microscopic procPSSP has been drlying the development of the statistical mechanical theory of sony-body Systons. Neile most of the fundamental questions associated with veversible pro cesses have yet to be answered to the satisfaction of all mysicists, the theiry tas ontained valuable results for “down-to-sart” physics by giving molecular expr For those quantityes encountered to sacroscopic evotation Taws. Most of trose ques Clems concerning the general form of sacrassopic evolution aquacions, their features and symetrins, and they comme on with the milecular process can be and guste generally, independent of particular models, on different levels of ttan, each level being related co the chers by a hiarachical structure.
These cuestions cas be approached to an elegant manner by utilizing te profectis френатар сеститque, which will be presented te detall in this volume, This method is employee ta alive transport equations for the relaxation of the nean, Langevin equ tions for the fluctuations about the weae, and, further, on a more detailed level. Fokker-Planck and master suatsons. The relations between the various evslution euette will to discussed and the equations theeselves will be iThatrated by ap glying tres to specific models.
The emphasis of this article is of the unifying aspects of the Cifferent statis Sical mechanical theories of relaxation sa fluctuation in many-body retoms HON ever, the work coes not treat those approaches which tegin particularly close to the moleculer level, such as the Boltzmane cuation, because these aparsethes, of necessity, depend on details of particular models
I am grateful to the many collesques who have adtes to ey insights and under standing. In particular, sendabted to those with whom I have had the slessure of close collaturatiss. Eidlich, P. Tale, P., A. Brenes, and, espec ally, the late M.S. Sreen
Special thanks are also die ta ft. Maken whose suggestions and efforts as a co editor were rust helpful