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Statistical Mechanics, Kinetic Theory, and Stochastic Processes presents the statistical aspects of physics as a "living and dynamic" subject. In order to provide an elementary introduction to kinetic theory, physical systems in which particle-particle interaction can be neglected are considered. Transport phenomena in the free-molecular flow region for gases and the transport of thermal radiation are discussed. Discrete random processes such as random walk, binomial and Poisson distributions, and throwing of dice are studied by means of the characteristic function. Comprised of 11 chapters, this book begins with an introduction to the mass point gas as well as some elementary properties of space and velocity distributions. The discussion then turns to radiation and its interaction with an atom; probability, statistics, and conditional probability; intermolecular interactions; transport phenomena; and statistical thermodynamics. Molecular systems at low densities are also considered, together with non-ideal and real gases; liquids and solids; and stochastic processes, noise, and fluctuations. In particular, the response of atoms and molecules to perturbations and scattering by crystals, liquids, and high-pressure gases are examined. This monograph will be useful for undergraduate students, practitioners, and researchers in physics.
Aimed at graduate students, this book explores some of the core phenomena in non-equilibrium statistical physics. It focuses on the development and application of theoretical methods to help students develop their problem-solving skills. The book begins with microscopic transport processes: diffusion, collision-driven phenomena, and exclusion. It then presents the kinetics of aggregation, fragmentation and adsorption, where the basic phenomenology and solution techniques are emphasized. The following chapters cover kinetic spin systems, both from a discrete and a continuum perspective, the role of disorder in non-equilibrium processes, hysteresis from the non-equilibrium perspective, the kinetics of chemical reactions, and the properties of complex networks. The book contains 200 exercises to test students' understanding of the subject. A link to a website hosted by the authors, containing supplementary material including solutions to some of the exercises, can be found at www.cambridge.org/9780521851039.
Let us begin by quoting from the Preface to the author's Statistical Physics (Moscow, Nauka 1982; also published in English by Harwood in 1986): '''My God! Yet another book on statistical physics! There's no room on my bookshelves left!' Such emotionsare quite understandable. Beforejumping to conclusions, however, it would be worthwhile to read the Introduction and look through the table of contents. Then the reader will find that this book is totally different from the existing courses, fundamental and concise. ... We do not use the conventional division into statistical theories ofequilibrium and nonequilibrium states. Rather than that, the theory ofnonequilibrium state is the basis and the backbone oftheentirecourse. ... This approach allows us to develop a unified method for statistical description ofa very broadclassofsystems. ... The author certainly does not wish to exaggerate the advantages of the book, considering it asjustthe first attemptto create a textbookofa new kind." The next step in this direction was the author's Turbulent Motion and the Structure of Chaos (Moscow, Nauka 1990; Kluwer Academic Publishers 1991). This book is subtitled A New Approach to the Statistical Theory of Open Systems. Naturally, the "new approach" is not meant to defy the consistent and efficient methods of the conventional statistical theory; itshould be regarded as auseful reinforcementofsuch methods.
This book introduces an approach to protein folding from the point of view of kinetic theory. There is an abundance of data on protein folding, but few proposals are available on the mechanism driving the process. Here, presented for the first time, are suggestions on possible research directions, as developed by the author in collaboration with C C Lin.The first half of this invaluable book contains a concise but relatively complete review of relevant topics in statistical mechanics and kinetic theory. It includes standard topics such as thermodynamics, the Maxwell-Boltzmann distribution, and ensemble theory. Special discussions include the dynamics of phase transitions, and Brownian motion as an illustration of stochastic processes.The second half develops topics in molecular biology and protein structure, with a view to discovering mechanisms underlying protein folding. Attention is focused on the energy flow through the protein in its folded state. A mathematical model, based on the Brownian motion of coupled harmonic oscillators, is worked out in the appendix.
This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statistical mechanics. This will interest specialists of various fields, especially the (classical and quantum) plasma physics. However, quantum physics — to which a major part is devoted — will be of more interest since, not only it applies to quantum plasma physics, but also to nuclear matter and to strong magnetic field, cosmology, etc. Although the domain of gauge theory is not covered in this book, the topic is not completely forgotten, in particular in the domain of plasma physics. This book is particularly readable for graduate students and a fortiori to young researchers for whom it offers methods and also appropriate schemes to deal with the current problems encountered in astrophysics, in strong magnetic, in nuclear or even in high energy physics.
This book presents both the fundamentals and the major research topics in statistical physics of systems out of equilibrium. It summarizes different approaches to describe such systems on the thermodynamic and stochastic levels, and discusses a variety of areas including reactions, anomalous kinetics, and the behavior of self-propelling particles.
This book is a printed edition of the Special Issue "Thermodynamics and Statistical Mechanics of Small Systems" that was published in Entropy
The author investigates athermal fluctuation from the viewpoints of statistical mechanics in this thesis. Stochastic methods are theoretically very powerful in describing fluctuation of thermodynamic quantities in small systems on the level of a single trajectory and have been recently developed on the basis of stochastic thermodynamics. This thesis proposes, for the first time, a systematic framework to describe athermal fluctuation, developing stochastic thermodynamics for non-Gaussian processes, while thermal fluctuations are mainly addressed from the viewpoint of Gaussian stochastic processes in most of the conventional studies. First, the book provides an elementary introduction to the stochastic processes and stochastic thermodynamics. The author derives a Langevin-like equation with non-Gaussian noise as a minimal stochastic model for athermal systems, and its analytical solution by developing systematic expansions is shown as the main result. Furthermore, the a uthor shows a thermodynamic framework for such non-Gaussian fluctuations, and studies some thermodynamics phenomena, i.e. heat conduction and energy pumping, which shows distinct characteristics from conventional thermodynamics. The theory introduced in the book would be a systematic foundation to describe dynamics of athermal fluctuation quantitatively and to analyze their thermodynamic properties on the basis of stochastic methods.
This text presents statistical mechanics and thermodynamics as a theoretically integrated field of study. It stresses deep coverage of fundamentals, providing a natural foundation for advanced topics. The large problem sets (with solutions for teachers) include many computational problems to advance student understanding.