Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

27 results

Page 1 of 2

Thermodynamic Formalism
  • The Mathematical Structure of Equilibrium Statistical Mechanics
  • 2nd edition
  • David Ruelle
  • Published online:
    15 January 2010
    Print publication:
    25 November 2004
  • Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. It is aimed at mathematicians interested in ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems, notably Anosov diffeomorphisms and flows. It is also of interest to theoretical physicists concerned with the conceptual basis of equilibrium statistical mechanics. The level of the presentation is generally advanced, the objective being to provide an efficient research tool and a text for use in graduate teaching. Background material on mathematics has been collected in appendices to help the reader. Extra material is given in the form of updates of problems that were open at the original time of writing and as a new preface specially written for this new edition by the author.

  • Introduction

  • David Ruelle, Institut des Hautes Études Scientifiques, France
  • Book:
    Thermodynamic Formalism
    Published online:
    15 January 2010
    Print publication:
    25 November 2004, pp 1-10

  • Summary

    Generalities

    The formalism of equilibrium statistical mechanics — which we shall call thermodynamic formalism — has been developed since G. W. Gibbs to describe the properties of certain physical systems. These are systems consisting of a large number of subunits (typically 1027) like the molecules of one liter of air or water. While the physical justification of the thermodynamic formalism remains quite insufficient, this formalism has proved remarkably successful at explaining facts.

    In recent years it has become clear that, underlying the thermodynamic formalism, there are mathematical structures of great interest: the formalism hints at the good theorems, and to some extent at their proofs. Outside of statistical mechanics proper, the thermodynamic formalism and its mathematical methods have now been used extensively in constructive quantum field theory and in the study of certain differentiable dynamical systems (notably Anosov diffeomorphisms and flows). In both cases the relation is at an abstract mathematical level, and fairly inobvious at first sight. It is evident that the study of the physical world is a powerful source of inspiration for mathematics. That this inspiration can act in such a detailed manner is a more remarkable fact, which the reader will interpret according to his own philosophy.

    The main physical problem which equilibrium statistical mechanics tries to clarify is that of phase transitions. When the temperature of water is lowered, why do its properties change first smoothly, then suddenly as the freezing point is reached?

Page 1 of 2