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On Dobrushin's Way. From Probability Theory to Statistical Physics
Fellow Russian mathematicians discuss and extend the works of Dobrushin (1929-95,), who worked in many areas of mathematics, but had deepest influence on mathematical physics and was one of the founders of the rigorous study of statistical physics. The 15 technical papers are flanked by a short biography and recollections by colleagues and students. The topics include the lower spectral branch of the generator of the stochastic dynamics for the classical Heisenberg model, non-symmetric simple random walks along orbits of ergodic automorphisms, the Cramer transform and large deviations on three- dimensional Lobachevsky space, and dynamics of Ising-spin systems at zero temperature. No index is provided. Annotation copyrighted by Book News, Inc., Portland, OR.
Statistical Mechanics and Fractals
This book is composed of two texts, by R.L. Dobrushin and S. Kusuoka, each representing the content of a course of lectures given by the authors. They are pitched at graduate student level and are thus very accessible introductions to their respective subjects for students and non specialists. CONTENTS: R.L. Dobrushin: On the Way to the Mathematical Foundations of Statistical Mechanics.- S. Kusuoka: Diffusion Processes on Nested Fractals.
Multicomponent Random Systems
"The present book contains a set of original scientific researches devoted to various problems of the theory of dynamical systems and multicomponent random systems, both theoretical and motivated by concrete applications." - Preface
Probability Contributions to Statistical Mechanics
Physics has always been a fertile source of new mathematical notions and ideas, and in the past decade the stream of ideas from physics to mathematics has increased dramatically. The subfield of statistical mechanics is no exception. Containing papers written by representatives of the Moscow school of mathematical statistical mechanics, this volume illustrates certain aspects of the developing interaction between statistical mechanics on the one hand and the theories of probability and of dynamical systems on the other. Included here are papers on random walks, phase transition phenomena for Gibbs random fields, the existence of nonstandard motion integrals in statistical physics models, and the Frenkel-Kontorova model.
Mathematical Problems of Statistical Mechanics and Dyanamics
Approach your problems from the It isn't that they can't see the solution. right end and begin with the answers. It is that they can't see the problem. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate ar...
Entropy, Large Deviations, and Statistical Mechanics
From the reviews: "... Each chapter of the book is followed by a notes section and by a problems section. There are over 100 problems, many of which have hints. The book may be recommended as a text, it provides a completly self-contained reading ..." --S. Pogosian in Zentralblatt für Mathematik
Statistical Mechanics of Lattice Systems
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Making Sense of Statistical Mechanics
Many people, including physicists, are confused about what the Second Law of thermodynamics really means, about how it relates to the arrow of time, and about whether it can be derived from classical mechanics. They also wonder what entropy really is: Is it all about information? But, if so, then, what is its relation to fluxes of heat? One might ask similar questions about probabilities: Do they express subjective judgments by us, humans, or do they reflect facts about the world, i.e. frequencies. And what notion of probability is used in the natural sciences, in particular statistical mechanics? This book addresses all of these questions in the clear and pedagogical style for which the author is known. Although valuable as accompaniment to an undergraduate course on statistical mechanics or thermodynamics, it is not a standard course book. Instead it addresses both the essentials and the many subtle questions that are usually brushed under the carpet in such courses. As one of the most lucid accounts of the above questions, it provides enlightening reading for all those seeking answers, including students, lecturers, researchers and philosophers of science.
From Markov Chains to Non-Equilibrium Particle Systems
' This book is representative of the work of Chinese probabilists on probability theory and its applications in physics. It presents a unique treatment of general Markov jump processes: uniqueness, various types of ergodicity, Markovian couplings, reversibility, spectral gap, etc. It also deals with a typical class of non-equilibrium particle systems, including the typical Schlögl model taken from statistical physics. The constructions, ergodicity and phase transitions for this class of Markov interacting particle systems, namely, reaction–diffusion processes, are presented. In this new edition, a large part of the text has been updated and two-and-a-half chapters have been rewritten. The...
