This thesis presents an in-depth study of statistical mechanical systems having microcanonical equilibrium properties, i.e., energy-dependent equilibrium properties, which cannot be put in correspondence with their canonical or temperature-dependent equilibrium properties. A general theory of these systems which focuses both on the thermodynamic and macrostate levels of description of systems is presented along the lines of a number of rigorous results derived recently by Ellis, Haven and Turkington (Journal of Statistical Physics, 2000). Several new results are also presented which relate the appearance of nonequivalent microcanonical and canonical properties with first-order (discontinuous) phase transitions and with nonequilibrium properties of systems. / Since the material presented in this thesis dwells on many elements of large deviations theory which are not familiar to physicists, a self-contained introduction to this theory has been included here. The presentation of the theory of nonequivalent microcanonical and canonical properties follows together with explicit computations carried out in the context of two simple spin models: a first original model involving a mixture of completely correlated and completely uncorrelated spins, and another model known as the mean-field Blume-Emery-Griffiths model.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.84851 |
| Date | January 2003 |
| Creators | Touchette, Hugo |
| Contributors | Crepeau, Claude (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 002095290, proquestno: AAINQ98383, Theses scanned by UMI/ProQuest. |
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