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Unformatted text preview: Part I STATISTICAL PHYSICS 1 Statistical Physics Version 0202.1, October 2002 In this first part of the book we shall study aspects of classical statistical physics that ev- ery physicist should know but are not usually treated in elementary thermodynamics courses. This study will lay the microphysical (particle-scale) foundations for the continuum physics of Parts IIVI. Throughout, we shall presume that the reader is familiar with elementary thermodynamics, but not with other aspects of statistical physics. As a central feature of our approach, we shall emphasize the intimate connections between the relativistic formulation of statistical physics and its nonrelativistic limit, and between quantum statistical physics and the classical theory. Chapter 2 will deal with kinetic theory , which is the simplest of all formalisms for studying systems of huge numbers of particles (e.g., molecules of air, or neutrons diffusing through a nuclear reactor, or photons produced in the big-bang origin of the Universe). In kinetic theory the key concept is the distribution function or number density of particles in phase space, N ; i.e., the number of particles per unit 3-dimensional volume of ordinary space and per unit 3-dimensional volume of momentum space. Despite first appearances, N turns out to be a geometric, frame-independent entity. This N and the laws it obeys provide us with a means for computing, from microphysics, a variety of quantities that characterize macroscopic, continuum physics: mass density, thermal energy density, pressure, equations of state, thermal and electrical conductivities, viscosities, diffusion coefficients, ... . Chapter 3 will deal with the foundations of statistical mechanics . Here our statistical study will be rather more sophisticated than in Chap. 2: We shall deal with ensembles of physical systems. Each ensemble is a (conceptual) collection of a huge number of physical systems that are identical in the sense that they have the same degrees of freedom, but different in that their degrees of freedom may be in different states. For example, the systems in an ensemble might be balloons that are each filled with 10 23 air molecules so each is describable by 3 10 23 coordinates (the x , y , z of all the molecules) and 3 10 23 momenta (the p x , p y , p z of all the molecules). The state of one of the balloons is fully described, then, by 6 10 23 numbers. We introduce a distribution function N which is a function of these 6 10 23 different coordinates and momenta, i.e., it is defined in a phase space with 6 10 23 dimensions. This distribution function tells us how many systems in our ensemble lie in a unit volume of that phase space. Using this distribution function we will study such issues as the statistical meaning of entropy, the statistical origin of the second law of thermodynamics, the statistical meaning of thermodynamic equilibrium, and the evolution of ensembles into thermodynamic equilibrium....
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