In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis - the form of the microcanonical density matrix - this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications to critical dynamics, as well as fundamental considerations of irreversibility, are discussed. The text will be useful for advanced students of physics and other natural sciences; a basic knowledge of quantum mechanics is presumed.

Klappentext

This unique and consistent mathematical treatise contains a deductive description of equilibrium statistics and thermodynamics. The most important elements of non-equilibrium phenomena are also treated. In addition to the fundamentals, the text tries to show how large the area of statistical mechanics is and how many applications can be found here. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications in critical dynamics, as well as fundamental thoughts of irreversibility are discussed. The text will be useful for advanced students in physics and other sciences who have profound knowledge of quantum mechanics.

Inhalt

1. Basic Principles.- 2. Equilibrium Ensembles..- 3. Thermodynamics.- 4. Ideal Quantum Gases.- 5. Real Gases, Liquids, and Solutions.- 6. Magnetism.- 7. Phase Transitions, Renormalization Group Theory, and Percolation.- 8. Brownian Motion, Equations of Motion and the Fokker-Planck Equations.- 9. The Boltzmann Equation.- 10. Irreversibility and the Approach to Equilibrium.- Appendix..- A. Nernst's Theorem (Third Law)..- A.1 Preliminary Remarks on the Historical Development of Nernst's Theorem.- A.2 Nernst's Theorem and its Thermodynamic Consequences.- A.3 Residual Entropy, Metastability, etc..- B. The Classical Limit and Quantum Corrections.- B.1 The Classical Limit..- B.2 Calculation of the Quantum-Mechanical Corrections.- C. The Perturbation Expansion.- D. The Riemann ?-Function and the Bernoulli Numbers.- E. Derivation of the Ginzburg-Landau Functional.- F. The Transfer Matrix Method..- G. Integrals Containing the Maxwell Distribution.- H. Hydrodynamics.- H.1 Hydrodynamic Equations, Phenomenological Discussion.- H.2 The Kubo Relaxation Function..- H.3 The Microscopic Derivation of the Hydrodynamic Equations.- I. Units and Tables..