A New Thermodynamics from Nuclei to Stars III

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. It is further shown that the second law is a natural consequence of the statistical nature of thermodynamics which describes all systems with the same -- redundant -- set of few control parameters simultaneously. It has nothing to do with the thermodynamic limit. It even works in systems which are by far {\em larger} than any thermodynamic "limit".

22 pages, 11 figures, treatment of the second law included

Cited by in corpus (7)

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• Influence of complete energy sorting on the characteristics of the odd-even effect in fission-fragment element distributions
• Tsallis entropy induced metrics and CAT(k) spaces
• Microcanonical Thermostatistics as Foundation of Thermodynamics. The microscopic origin of condensation and phase separations
• Understand the thermometry of hot nuclei from the energy spectra of light charged particles
• Reconciliation of Statistical Mechanics and Astro-Physical Statistics. The errors of conventional canonical thermostatistics
• A Microcanonical Inflection Point Analysis via Parametric Curves and its Relation to the Zeros of the Partition Function