“The importance of knowledge consists not only in its direct practical utility but also in the fact the it promotes a widely contemplative habit of mind; on this ground, utility is to be found in much of the knowledge that is nowadays labelled ‘useless’. ” Bertrand Russel, In Praise of Idleness, London (1935) “Why are scientists in so many cases so deeply interested in their work ? Is it merely because it is useful ? It is only necessary to talk to such scientists to discover that the utilitarian possibilities of their work are generally of secondary interest to them. Something else is primary. ” David Bohm, On creativity, Abingdon (1996) In this volume, the dynamical critical behaviour of many-body systems far from equilibrium is discussed. Therefore, the intrinsic properties of the - namics itself, rather than those of the stationary state, are in the focus of 1 interest. Characteristically, far-from-equilibrium systems often display - namical scaling, even if the stationary state is very far from being critical. A 1 As an example of a non-equilibrium phase transition, with striking practical c- sequences, consider the allotropic change of metallic ?-tin to brittle ?-tin. At o equilibrium, the gray ?-Sn becomes more stable than the silvery ?-Sn at 13. 2 C. Kinetically, the transition between these two solid forms of tin is rather slow at higher temperatures. It starts from small islands of ?-Sn, the growth of which proceeds through an auto-catalytic reaction.

This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.

Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.

This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena, examining simulation results in detail. Later chapters discuss absorbing-state transitions, and examine a variety of systems subject to dynamic disorder. The book discusses the effects of multiparticle rules, nonunique absorbing-states and conservation laws, as well as the use of methods such as mean-field theory, Monte Carlo simulation and the concept of universality. It also includes detailed references and examples using simple respresentations of nature to describe real systems.

This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. All equations and deductions are included.

The publication of this second edition was motivated by several facts. First of all, the first edition had been sold out in less than one year. It had found excellent critics and enthusiastic responses from professors and students welcoming this new interdisciplinary approach. This appreciation is reflected by the fact that the book is presently translated into Russian and Japanese also. I have used this opportunity to include some of the most interesting recent developments. Therefore I have added a whole new chapter on the fascinating and rapidly growing field of chaos dealing with irregular motion caused by deterministic forces. This kind of phenomenon is presently found in quite diverse fields ranging from physics to biology. Furthermore I have included a section on the analytical treatment of a morphogenetic model using the order parameter concept developed in this book. Among the further additions, there is now a complete description of the onset of ultrashort laser pulses. It goes without· saying that the few minor mis prints or errors of the first edition have been corrected. I wish to thank all who have helped me to incorporate these additions.

A comprehensive and pedagogical text on nonequilibrium statistical physics, covering topics from random walks to pattern formation.