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A New Thermodynamics, From Nuclei to Stars II

D. H. E. Gross
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Abstract

Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann's principle, e^S=tr(δ(E-H)), its geometrical size is related to the entropy S(E,N,...). This definition does not invoke any information theory, no thermodynamic limit, no extensivity, and no homogeneity assumption, as are needed in conventional (canonical) thermo-statistics. Therefore, it describes the equilibrium statistics of extensive as well of non-extensive systems. Due to this fact it is the general and fundamental definition of any classical equilibrium statistics. It can address nuclei and astrophysical objects as well. As these are not described by the conventional extensive Boltzmann-Gibbs thermodynamics, this is a mayor achievement of statistical mechanics. Moreover, all kind of phase transitions can be distinguished sharply and uniquely for even small systems. In contrast to the Yang-Lee singularities in Boltzmann-Gibbs canonical thermodynamics phase-separations are well treated.

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D. H. E. Gross. 2003-06-19. A New Thermodynamics, From Nuclei to Stars II. https://arxiv.org/abs/cond-mat/0306499

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