A New Thermodynamics, From Nuclei to Stars

TL;DR

This paper presents a fundamental approach to equilibrium thermodynamics based on microcanonical ensemble, applicable to both extensive and non-extensive systems, from nuclei to stars, without relying on traditional assumptions.

Contribution

It introduces a geometrical, information-theory-independent definition of entropy that applies universally, including small and astrophysical systems, and clarifies phase transitions without thermodynamic limits.

Findings

Defines entropy via phase space volume, independent of thermodynamic limit.

Applicable to small, non-extensive, and astrophysical systems.

Sharp distinction of phase transitions even in small systems.

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, $e^S=tr(\delta(E-H))$, 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 {\em fundamental} definition of any classical equilibrium statistics. It can address nuclei and astrophysical objects as well. All kind of phase transitions can be distinguished sharply and uniquely for even small systems. For transitions in nuclear physics the scaling to an hypothetical uncharged nuclear matter with an $N/Z-$ ratio like realistic nuclei is not needed.