Mathematical Sciences: Exact Results in Statistical Mechanics

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One of the fundamental problems in statistical mechanics is to bridge the gap between macroscopic, phenomenological laws - e.g., hydrodynamical and kinetic equations -and the underlying microscopic description involving interactions between a large number of particles. The delicacy of the problem can be appreciated if we consider that the microscopic laws are (time) reversible while the macroscopic are irreversible (Zermelo's "paradox"). Professor Goldstein plans to continue his investigations into problems- e.g., the derivations of diffusion equations, stochastic behavior, and convergence to equilibrium and the steady state- whose solutions would narrow this gap.