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Session I" STATISTICAL MECHANICS EIGENMODES OF CLASSICAL FLUIDS IN THERMAL EQUILIBRIUM E. G. D. Cohen The Rockefeller University 1230 York Avenue New York, NY 10021 Abstract The eigenmodes of a classical fluid in thermal equilibrium are discussed. wavelengths and times, they can be computed from linear hydrodynamic are then the hydrodynamic diffusion modes, in particular, the heat mode, of heat in the fluid and two sound modes. For long equations. which For short wavelengths they can be derived from linear kinetic operators. For low densities, extensions of the kinetic analogues of the heat and sound modes. the e x t e n d e d extensions of the Boltzmann operator heat mode, while next of the sound modes. is used. the and times the linear Boltzmann operator can be employed and the three most important eigenmodes a generalization They describes are direct For high densities, The most important eigenmode in i m p o r t a n c e come two e i g e n m o d e s These three extended hydrodynamic that is are modes can be used to obtain the light and neutron spectra of fluids and vice versa. I. Introduction In this paper, classical particles. the one I am c o n c e r n e d statistical with mechanics the t r a n s i t i o n for m a c r o s c o p i c The basic question then is: hand, the d y n a m i c s from classical systems, mechanics consisting how does one make a c o n n e c t i o n of the many particles between, here liquids, The most to a d i s c u s s i o n of this question for classical fluids, familiar macroscopic properties properties. Thus description of a system the o b s e r v e d with local involves the identification statistically averaged is c o n n e c t e d but also distribution with function, and time velocity equilibrium therefore systems, kinetic equations. or the of p a r t i c l e s ~n thermal equilibrium, and A finer uses distribution description functions, which gives the average number average number of pairs systems properties. velocities a certain microscopic or the local with the average momentum density at this point and similarly for other local thermodynamic positions of observed number density at a particular point in the fluid is identified with the average number of particles at this point point I restrict i.e., gases and and what follows has been written with these systems in mind. macroscopic velocity on in the system, and on the other hand, the physically observed properties of the system in the laboratory? myself to of very many their they pair of p a r t i c l e s distribution at two points involving with not only like the single particle at a p a r t i c u l a r function, certain that gives the velocities. In