The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of statistical mechanics incorporating both approaches, by redefining equilibrium not as a binary property but as a continuous property measured by the Boltzmann entropy and by introducing the idea of thermodynamic-like behaviour for the Boltzmann entropy. The Kac ring model is used as an example (...) to test the proposals. (shrink)

This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down after sufficient time has gone by. Time dependent phenomena are beyond the scope of this paper. While thermodynamics is firmly rooted in statistical physics, equilibrium configurations, stability criteria and the destabilizing effect of fluctuations are all expressed in terms of thermodynamic functions. The work is not a review paper but (...) a pedagogical introduction which may interest theoreticians in astronomy and astrophysicists. It contains sufficient mathematical details for the reader to redo all calculations. References are only to seminal works or readable reviews. Delicate mathematical problems are mentioned but are not discussed in detail. (shrink)

This paper discusses the mistake of understanding the laws and concepts of thermodynamics too literally in the foundations of statistical mechanics. Arguing that this error is still made in subtle ways, the article explores its occurrence in three examples: the Second Law, the concept of equilibrium and the definition of phase transitions.

Two of the world's leading astrophysicists, James Binney and Scott Tremaine, here present a comprehensive review of the theory of galactic dynamics at a level suitable for both graduate students and researchers. Their work in this volume describes our present understanding of the structure and dynamics of stellar systems such as galaxies and star clusters. Nicknamed "the Bible of galactic dynamics," this book has become a classic treatise, well known and widely used by researchers and students of galactic astrophysics and (...) stellar dynamics. Praised for its modern approach, as well as for the rigor and exemplary clarity with which the authors handle the material in this book, Galactic Dynamics includes classic results and data while also reflecting the many recent developments in the field. The authors maintain an effective style of exposition throughout, keeping clear what is present knowledge and what is still speculation, while allowing the reader to grasp an overview of the subject before following through with the mathematical detail. Most of the astronomical community since the late 1980s was introduced to galactic dynamics through Galactic Dynamics, and it remains the most widely used graduate textbook in galactic astrophysics today. No other book gathers together and presents our current understanding of the field in such a clear and concise way. Through this approach, Binney and Tremaine succeeded in creating a classic reference of enormous pedagogic value. (shrink)