Titlebook: Methods in Statistical Mechanics; A Modern View Osvaldo Civitarese,Manuel Gadella Textbook 2020 The Editor(s) (if applicable) and The Autho

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The Liouville Equation,Explores the principles of statistical mechanics in terms of geometry, as anticipated by Bogolubov, and the role of dynamical variables in the statistical properties of a system, either classical or quantum. The evolution of these variables is described by a non-linear system of 2n differential equations.

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Canonical Distributions and Thermodynamic Functions,Specializes in the connections between statistical ensembles, from the point of view of the Hamiltonian dynamics and from the operator approach. The chapter is devoted to the unification of both of these schemes, paying attention to the definition of thermodynamical observables in the context of static and quasi-static processes.

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t of the science of materials with a low-dimensional and aperiodic structure has again highlighted the problem of modeling the nucleation of growth and deformation of lattice structures. When considering structural changes in modified materials, one has to face the contradictions between the infinit

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An Introduction to Statistical Mechanics, the notion of probabilities and thermal equilibrium in the Gibbs approach. This formulation applies to both classical and quantum systems. The concept of probability is illustrated by solving a system with discrete energy levels. The material included in the chapter is mathematically self-contained

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The Role of Dynamics in Statistical Mechanics,pretation of statistical mechanics. The motivation is obvious, since the probabilistic conception of statistical mechanics is based on the knowledge of the exact energy levels of the system under study, something which in practice is restricted to very few examples. Following the Feynman approach, w