A Kinetic View of Statistical Physics

Title: A Kinetic View of Statistical Physics

Authors: Pavel L. Krapivsky, Sidney Redner, and Eli Ben-Naim

Publisher: Cambridge University Press

Publication date: October 2010

Table of Contents: [pdf]

Errata: [pdf]

Solution Manual: available to instructors (see publisher website)

Details: 500 pages · 220 Problems · 125 Illustrations

Purchase: Cambridge, Amazon

Preview: Cambridge, Google

About the book: 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.

• Enables students to develop their problem-solving skills by detailing a wide range of problems
• Examines systems far from equilibrium, where results can be derived for their dynamical evolution
• Focuses on theoretical methods to solve concrete non-equilibrium statistical physics problems

Translation: A translation to Russian by Alexander Povolotsky is forthcoming.

Reviews:

Mathematical Reviews: Alexander Orlov

Contemporary Physics: Stig Stenholm

"Non-equilibrium statistical mechanics has so many applications and is strewn with so many different tricks and treats that the only way to teach the subject is through examples. Krapivsky, Redner, and Ben-Naim have written a beautiful book that elegantly covers several of these examples, some classic, others at the boundaries of research. Their target readership is physicists and applied mathematicians, but includes computer scientists, biologists and engineers. Methinks that good students in economics would be well advised to read some chapters of this book, for I am convinced that several breakthroughs in their field will hinge upon concepts and methods from non-equilibrium statistical mechanics."
J. P. Bouchaud, Chairman of Capital Fund Management (Paris) and Statistical Mechanics Professor, Ecole Polytechnique

"Our understanding of nonequilibrium statistical physics and complex systems has advanced at a rapid pace over the past decade, but so far there has been a lack of comprehensive textbooks suited to introduce graduate students into the field. This wonderful book fills this need in an admirable way. Written in the uniquely elegant and accessible style that also characterizes the authors' original scientific work, the book takes the reader gently from the most elementary concepts to the forefront of current research. The topics and their level of presentation are carefully chosen, and they are complemented by a large number of instructive exercises. A particularly nice feature is the highlighted boxes which introduce specific mathematical techniques where they are needed. I am certain that this book will be used as a standard text in graduate courses for a long time to come."
Joachim Krug, University of Cologne

"This is an excellent pedagogical introduction to a broad variety of modern topics in nonequilibrium statistical physics. It includes discussions on fundamental processes in nature such as diffusion, collision, aggregation and fragmentation but also covers applied topics such as population dynamics and evolution of networks. The text is lucid with plenty of examples and exercises - a must read for a graduate student wanting to work in this area."
Satya Majumdar, CNRS, Universite de Paris-Sud

Contents:

Chapter 1: Aperitifs

Diffusion · Single-Species Annihilation/Coalescence · Two-Species Annihilation

Chapter 2: Diffusion

The Probability Distribution · Central Limit Theorem · Walks with Broad Distributions · Application to Gravity: The Holtsmark Distribution · First-Passage Properties · Exit Probabilities and Exit Times · Reaction-Rate Theory · The Langevin Approach · Application to Surface Growth

Chapter 3: Collisions

Kinetic Theory · The Lorentz Gas · Lorentz Gas in an External Field Collisional Impact · Maxwell Molecules and Very Hard Particles · Inelastic Gases Ballistic Agglomeration · Single-Lane Traffic · Application to Surface Growth

Chapter 4: Exclusion

Symmetric Exclusion Process · Asymmetric Exclusion Process · Hydrodynamic Approach · Microscopic Approach · Open Systems

Chapter 5: Aggregation

The Master Equations · Exact Solution Methods · Gelation · Scaling · Aggregation with Input · Exchange-Driven Growth

Chapter 6: Fragmentation

Binary Fragmentation · Planar Fragmentation · Reversible Polymerization · Collisional Fragmentation

Chapter 7: Adsorption

Random Sequential Adsorption in One Dimension · Phase Space Structure · Adsorption in Higher Dimensions · Reversible Adsorption · Polymer Translocation

Chapter 8: Spin dynamics

Phenomenology of Coarsening · The Voter Model · Ising-Glauber Model · Mean-Field Approximation · Glauber Dynamics in One Dimension · Glauber Dynamics in Higher Dimensions · Spin-Exchange Dynamics · Cluster Dynamics

Chapter 9: Coarsening

Models · Free Evolution · Case Studies in Non-Conservative Dynamics · Final States · Defects · Conservative Dynamics · Extremal Dynamics · Nucleation and Growth

Chapter 10: Disorder

Disordered Spin Chain · Random Walk in a Random Potential · Random Walk in Random Velocity Fields

Chapter 11: Hysteresis

Homogeneous Ferromagnets · Perturbation Analysis · Disordered Ferromagnets · Mean-field Model · Hysteresis in the Random-Field Ising Chain

Chapter 12: Population dynamics

Continuum Formulation · Discrete Reactions · Small Fluctuation Expansion · Large Fluctuations

Chapter 13: Diffusive reactions

Role of the Spatial Dimension · The Trapping Reaction · Two-Species Annihilation · Single-Species Reactions in One Dimension · Reactions in Spatial Gradients

Chapter 14: Complex networks

Non-Lattice Networks · Evolving Random Graphs · Random Recursive Trees · Preferential Attachment · Fluctuations in Networks