phys212ln1 - Physics 212 Statistical mechanics II Fall 2006...

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Physics 212: Statistical mechanics II, Fall 2006 Lecture I A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts. A. Einstein Let us start with an overview of the material to be covered this semester. You, the reader, should by now have had a solid undergraduate semester of basic statistical mechanics, including such concepts as entropy and the laws of thermodynamics together with applications to ideal classical and quantum gases. There is a great deal more to the story, including both new fundamental concepts and a wealth of applications. Many of the terms and ideas in this overview may be quite unfamilar, but should become much clearer during the course of the semester. A note on textbooks: I did not choose a single textbook for the course not because of a shortage of good textbooks but because there are several good textbooks for the first and second parts of the course, and any of these will be adequate. Lecture notes are no substitute for a good textbook, though, and you’ll probably want to have access to a book for Part I (nonequilibrium statistical mechanics) and Part II (introduction to RG and critical phenomena). Part III (selected applications of parts I and II) will consist largely of recent examples for which there is not a good textbook. Some general texts for Part I which contain kinetic theory are K. Huang, Statistical mechanics . R. Balescu, Equilibrium and nonequilibrium statistical mechanics L. D. Landau and E. M. Lifshitz, Statistical mechanics and Physical kinetics A useful reference on the fluctuation-dissipation theorem is R. Kubo, M. Toda, N. Hashitsume, Statistical physics II (Nonequilibrium) A nice small book for Part II (critical phenomena and RG) is J. Cardy, Scaling and renormalization in statistical physics Others are S.-K. Ma, Statistical mechanics N. Goldenfeld, Lectures on phase transitions and the renormalization group , which has some useful material on dynamic phenomena. The first few lectures will study how entropy, temperature, and other thermodynamic equilib- rium quantities emerge from microscopic equations of motion (the problem of generalized kinetic theory or hydrodynamics ). Understanding the approach to thermodynamic equilibrium at a high 1
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level of rigor is a difficult mathematical challenge, but here we will be content with the standard physics arguments dating back to Boltzmann, Gibbs, and others. Understanding kinetic theory will let us understand a bit better where the following quantities come from: S = log Ω = i - p i log p i kT = ∂S ∂E - 1 (1) Let’s start with the entropy S . In the above formulas for S , Ω is the number of equally likely states in the first expression, and p i
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