Titlebook: Lectures on the Mechanical Foundations of Thermodynamics; Michele Campisi Book 20211st edition The Editor(s) (if applicable) and The Autho

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2191-5423 action and complications.Includes complements and exercises This brief provides a modern pedagogical exposition of the mechanical approach to statistical mechanics initiated by Boltzmann with his early works (1866-1871). Despite the later contribution by Helmholtz, Boltzmann himself (1884-1887), Gib

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The Grandcanonical Ensemble,es, this as well provides a good model of thermodynamics in the sense that it generates a conservative thermodynamic field. We illustrate this ensemble with the ideal gas, of which we calculate particle and energy fluctuations. Here we discuss as well the so called Gibbs correct counting factor.

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The Canonical Ensemble,al gas thermodynamics within the canonical formalism, as well as general expressions linking correlation functions to response coefficients (i.e., the fluctuation-dissipation relations). We conclude with a discussion of the finite heat bath statistics, and the peculiar thermodynamic properties of logarithmic oscillators.

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978-3-030-87162-8The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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The Constitutive Statements of Thermodynamics,r fields, by introducing the central notion of thermodynamic field. The first and second laws dictate that this field is conservative and that there exist accordingly a thermodynamic potential, also known as the entropy. Massieu potentials and standard thermodynamic potentials are reviewed as well.

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Minimal Mechanical Model of Thermodynamics, the very Hamiltonian nature of the equation of motion in the case of a particle in a U-shaped potential. This result is known as the Helmholtz theorem. We shall illustrate this with the most minimal mechanical model of a thermodynamic system, namely a particle in a 1D box, and other examples.