**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

**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