This book concentrates on the properties of the stationary states in
chaotic systems of particles or fluids, leaving aside the theory of the
way they can be reached. The stationary states of particles or of fluids
(understood as probability distributions on microscopic configurations
or on the fields describing continua) have received important new ideas
and data from numerical simulations and reviews are needed. The starting
point is to find out which time invariant distributions come into play
in physics. A special feature of this book is the historical approach.
To identify the problems the author analyzes the papers of the founding
fathers Boltzmann, Clausius and Maxwell including translations of the
relevant (parts of) historical documents. He also establishes a close
link between treatment of irreversible phenomena in statistical
mechanics and the theory of chaotic systems at and beyond the onset of
turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the
author gives arguments intending to support strongly the viewpoint that
stationary states in or out of equilibrium can be described in a unified
way. In this book it is the "chaotic hypothesis", which can be seen as
an extension of the classical ergodic hypothesis to non equilibrium
phenomena, that plays the central role. It is shown that SRB - often
considered as a kind of mathematical playground with no impact on
physical reality - has indeed a sound physical interpretation; an
observation which to many might be new and a very welcome insight.
Following this, many consequences of the chaotic hypothesis are analyzed
in chapter 3 - 4 and in chapter 5 a few applications are proposed.
Chapter 6 is historical: carefully analyzing the old literature on the
subject, especially ergodic theory and its relevance for statistical
mechanics; an approach which gives the book a very personal touch. The
book contains an extensive coverage of current research (partly from the
authors and his coauthors publications) presented in enough detail so
that advanced students may get the flavor of a direction of research in
a field which is still very much alive and progressing. Proofs of
theorems are usually limited to heuristic sketches privileging the
presentation of the ideas and providing references that the reader can
follow, so that in this way an overload of this text with technical
details could be avoided.
