Foundations of Statistical Mechanics: Equilibrium Theory [Paperback]

In a certain sense this book has been twenty-five years in the writing, since I first struggled with the foundations of the subject as a graduate student. It has taken that long to develop a deep appreciation of what Gibbs was attempting to convey to us near the end of his life and to understand fully the same ideas as resurrected by E.T. Jaynes much later. Many classes of students were destined to help me sharpen these thoughts before I finally felt confident that, for me at least, the foundations of the subject had been clarified sufficiently. More than anything, this work strives to address the following questions: What is statistical mechanics? Why is this approach so extraordinarily effective in describing bulk matter in terms of its constituents? The response given here is in the form of a very definite point of view-the principle of maximum entropy (PME). There have been earlier attempts to approach the subject in this way, to be sure, reflected in the books by Tribus [Thermostat? ics and Thermodynamics, Van Nostrand, 1961], Baierlein [Atoms and Information Theory, Freeman, 1971], and Hobson [Concepts in Statistical Mechanics, Gordon and Breach, 1971].1 Introduction.- A. Physical Foundations.- Many Degrees of Freedom.- B. Kinetic Theory.- C. The Notion of Ensembles.- D. Ergodic Theory.- E. Critique.- Problems.- References.- 2 Theory of Probability.- A. Historical Background.- B. The Algebra of Probable Inference.- Axiomatic Formulation.- Extensions of the Theory.- Probabilities and Frequencies.- C. Calculus of Probable Inference.- Principle of Maximum Entropy.- Further Properties of SI.- Probabilities and Frequencies.- General Observations.- Problems.- References.- 3 Equilibrium Thermodynamics.- A. Canonical Ensemble.- B. Fluctuations.- Measured Values.- Measurable Fluctuations.- Stability of the Equilibrium State.- C. The Efficacy of Statistical Mechanics.- Macroscopic Uniformity.- Generalized Inverse Problems.- Infinite Volume Limit.- Problems.- References.lã&