A ’’nonstandard’’ approach to the thermodynamic limit. II. Weakly tempered potentials and neutral Coulomb systems

This article reviews developments in the foundations of statistical mechanics during the past ten years or so. The first section discusses how statistical concepts enter the treatment of deterministic mechanical systems, with particular reference to trajectory instabilities and to the KAM theorem. The second section deals with large systems: the thermodynamic limit and the theory of infinite systems. The third section deals with non-equilibrium statistical mechanics. Relativistic statistical mechanics is not covered. The bibliography contains about 500 references. This review was received in March 1979. Contents 1. Probability and mechanics . 1.1. The Gibbs ensemble . 1.2. Ergodicity and mixing . 1.3. Trajectory instabilities , 1.4. The KAM theorem and the stochastic transition 1.5. Quantum Gibbs ensembles 2.1. The connection with thermodynamics 2.2. Infinite systems . 3.1. Non-equilibrium ensembles 3.2. Dilute gases . 3.3. Master equations . 3.4. Cells and macroscopic variables 3.5. Non-equilibrium entropy . 3.6. Non-Hamiltonian dynamics and open systems Acknowledgments . References . 2. Large systems . . 3. Non-equilibrium statistical mechanics .

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A ’’nonstandard’’ approach to the thermodynamic limit. II. Weakly tempered potentials and neutral Coulomb systems

Abstract: Existence of the thermodynamic limit for disordered quantum Coulomb systems

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The Allure of Infinitesimals: Sergio Albeverio and Nonstandard Analysis

The Allure of Infinitesimals: Sergio Albeverio and Nonstandard Analysis

Chapter 7. Hyperfinite Lattice Models

Foundations of statistical mechanics

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