Quantum Statistical Mechanics

This book provides a clear and self-contained exposition of quantum statistical mechanics, focussing on the foundations. The unifying theme is the statistical entropy, as modified for quantum systems. From this is derived the conventional expressions for equilibrium quantum statistical mechanics, and, most exciting, their extension to non-equilibrium, time-dependent systems. A unified treatment of the equilibrium and non-equilibrium fields is given based upon the conservation laws, time symmetries, and the second law of thermodynamics. One theme of the book is the collapse of the wave function of an open quantum system, which leads to the Maxwell-Boltzmann probability operator, its relationship to the density matrix, and the von Neumann trace expression for a statistical average. A second theme is the development of the appropriate entropy for quantum systems, which, in conjunction with the second law, gives the stochastic, dissipative Schrdinger equation for an open quantum system and the fluctuation-dissipation theorem for the time propagator. A final theme is the derivation of the probability operator for non-equilibrium systems and irreversible processes, which lies at the cutting edge of modern research.