Описание
KRAPIVSKY: “FM” — 2010/5/17 — 20:36 — PAGE xi — #11
Preface
Statistical physics is an unusual branch of science. It is not defined by a specific subject
per se, but rather by ideas and tools that work for an incredibly wide range of problems.
Statistical physics is concerned with interacting systems that consist of a huge number of
building blocks – particles, spins, agents, etc. The local interactions between these elements
lead to emergent behaviors that can often be simple and clean, while the corresponding fewparticle systems can exhibit bewildering properties that defy classification. From a statistical
perspective, the large size of a system often plays an advantageous, not deleterious, role in
leading to simple collective properties.
While the tools of equilibrium statistical physics are well-developed, the statistical
description of systems that are out of equilibrium is less mature. In spite of more than
a century of effort to develop a formalism for non-equilibrium phenomena, there still do
not exist analogs of the canonical Boltzmann factor or the partition function of equilibrium
statistical physics. Moreover, non-equilibrium statistical physics has traditionally dealt with
small deviations from equilibrium. Our focus is on systems far from equilibrium, where
conceptually simple and explicit results can be derived for their dynamical evolution.
Non-equilibrium statistical physics is perhaps best appreciated by presenting wideranging and appealing examples, and by developing an array of techniques to solve these
systems. We have attempted to make our treatment self-contained, so that an interested
reader can follow the text with a minimum of unresolved methodological mysteries or
hidden calculational pitfalls. Our main emphasis is on exact analytical tools, but we also
develop heuristic and scaling methods where appropriate. Our target audience is graduate
students beyond their first year who have taken a graduate course in equilibrium statistical
physics and have had a reasonable exposure to mathematical techniques. We also hope that
this book will be accessible to students and researchers in computer science, probability
theory and applied mathematics, quantitative biological sciences, and engineering, because
a wide variety of phenomena in these fields also involve the time evolution of systems with
many degrees of freedom.
We begin with a few “aperitifs” – an abbreviated account of some basic problems along
with some hints at methods of solution. The next three chapters comprise the major theme
of transport processes. Chapter 2 introduces random walks and diffusion phenomena,
mechanisms that underlie much of non-equilibrium statistical physics. Next, we discuss
collision-driven phenomena in Chapter 3. We depart from the tradition of entirely focusing
on the Boltzmann equation and its application to hydrodynamics. Instead, we emphasize
pedagogically illuminating and tractable examples, such as the Lorentz gas and Maxwell
models. In Chapter 4, we give a brief overview of exclusion processes and the profound
consequences that exclusion has on transport and the spatial distribution of particles.
Детали
- Год издания
- 2010
- Format