Classical Equilibrium Thermostatistics, "Sancta sanctorum of Statistical Mechanics", From Nuclei to Stars

TL;DR

This paper advocates for the microcanonical ensemble as the fundamental and universal approach to classical equilibrium thermodynamics, applicable to systems of any size or interaction range, including nuclei and stars.

Contribution

It provides a geometrical and rigorous definition of equilibrium statistics that does not rely on thermodynamic limits or information theory, applicable to both extensive and non-extensive systems.

Findings

Microcanonical ensemble accurately describes phase transitions.

Phase space regions for phase separation are accessible in this framework.

No need for q-entropy or other generalized entropies.

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-Planck's principle, e^S=tr(\delta(E-H)), its geometrical size is related to the entropy S(E,N,V,...). This definition does not invoke any information theory, no thermodynamic limit, no extensivity, and no homogeneity assumption. Therefore, it describes the equilibrium statistics of extensive as well of non-extensive systems. Due to this fact it is the fundamental definition of any classical equilibrium statistics. It addresses nuclei and astrophysical objects as well. S(E,N,V,...) is multiply differentiable everywhere, even at phase-transitions. All kind of phase transitions can be distinguished harply and uniquely for even small systems. What is even more important, in contrast to the canonical theory, also the region of phase-space which corresponds to phase-separation is accessible, where the most interesting phenomena occur. No deformed q-entropy is needed for equilibrium. Boltzmann-Planck is the only appropriate statistics independent of whether the system is small or large, whether the system is ruled by short or long range forces.