A New Thermodynamics, From Nuclei to Stars II

TL;DR

This paper presents a fundamental approach to equilibrium statistical mechanics using the microcanonical ensemble, applicable to both extensive and non-extensive systems like nuclei and stars, without relying on traditional thermodynamic assumptions.

Contribution

It introduces a geometrical, information-theory-independent definition of entropy that applies universally, enabling accurate analysis of small and non-extensive systems and their phase transitions.

Findings

Defines entropy via phase space volume without thermodynamic limits

Successfully describes phase transitions in small systems

Addresses systems beyond traditional Boltzmann-Gibbs thermodynamics

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 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.