This page intentionally left blank EQUILIBRIUM AND NON-EQUILIBRIUM STATISTICAL THERMODYNAMICS This book gives a self-contained exposition at graduate level of topics that are generally considered fundamental in modern equilibrium and non-equilibrium sta- tistical thermodynamics. The text follows a balanced approach between the macroscopic (thermody- namic) and microscopic (statistical) points of view. The first half of the book deals with equilibrium thermodynamics and statistical mechanics. In addition to stan- dard subjects, such as the canonical and grand canonical ensembles and quantum statistics, the reader will find a detailed account of broken symmetries, critical phenomena and the renormalization group, as well as an introduction to numer- ical methods, with a discussion of the main Monte Carlo algorithms illustrated by numerous problems. The second half of the book is devoted to non-equilibrium phenomena, first following a macroscopic approach, with hydrodynamics as an im- portant example. Kinetic theory receives a thorough treatment through the analysis of the Boltzmann–Lorentz model and of the Boltzmann equation. The book con- cludes with general non-equilibrium methods such as linear response, projection method and the Langevin and Fokker–Planck equations, including numerical sim- ulations. One notable feature of the book is the large number of problems. Simple applications are given in 71 exercises, while the student will find more elaborate challenges in 47 problems, some of which may be used as mini-projects. This advanced textbook will be of interest to graduate students and researchers in physics. M ICHEL L E B ELLAC graduated from the Ecole Normale Sup ́ erieure and ob- tained a Ph.D. in Physics at the Universit ́ e Paris-Orsay in 1965. He was appointed Professor of Physics in Nice in 1967. He also spent three years at the Theory Di- vision at CERN. He has contributed to various aspects of the theory of elementary particles and recently has been working on the theory of the quark–gluon plasma. He has written several textbooks in English and in French. F ABRICE M ORTESSAGNE obtained a Ph.D. in high-energy physics at the Universit ́ e Denis Diderot of Paris in 1995, and then was appointed Ma ˆ ıtre de Conf ́ erences at the Universit ́ e de Nice–Sophia Antipolis. He has developed semi- classical approximations of wave propagation in chaotic systems and was one of the initiators of the ‘Wave Propagation in Complex Media’ research group. In 1998 he extended his theoretical research activities with wave chaos experiments in chaotic optical fibres and microwave billiards. G. G EORGE B ATROUNI obtained a Ph.D. in theoretical particle physics at the University of California at Berkeley in 1983 and then took a postdoctoral fel- lowship at Cornell University. In 1986 he joined Boston University and later the Lawrence Livermore National Laboratory. He became professor at the Universit ́ e de Nice–Sophia Antipolis in 1996. He was awarded the Onsager Medal in 2004 by the Norwegian University of Science and Technology. He has made important con- tributions in the development of numerical simulation methods for quantum field theories and many body problems, and in the study of quantum phase transitions and mesoscopic models of fracture. EQUILIBRIUM AND NON-EQUILIBRIUM STATISTICAL THERMODYNAMICS MICHEL LE BELLAC, FABRICE MORTESSAGNE AND G. GEORGE BATROUNI