Phase Transitions in Finite Systems
- 804 Downloads
In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermostatistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent.
KeywordsIsing Model Thermodynamical Limit Order Phase Transition Canonical Ensemble Phase Coexistence
Unable to display preview. Download preview PDF.
- 2.A. Katz, ‘Principles of statistical mechanics’ Freeman (1967)Google Scholar
- 3.S. Abe, Y. Okamoto, ‘Nonextensive statistical mechanics and its applications’, Lecture Notes in Physics vol.560 (2001)Google Scholar
- 4.R. Balian, ‘From microphysics to macrophysics’, Springer Verlag (1982)Google Scholar
- 9.L.D. Landau, E.M. Lifshitz, ‘Statistical Physics’, Pergamon Press (1980)Google Scholar
- 10.M.E. Fisher, ‘Critical phenomena’, Academic (1971)Google Scholar
- 26.T. Poston, I. Stewart, “Catastrophe Theory and its applications”, Pitman (1978)Google Scholar