Microcanonical Thermostatistics as Foundation of Thermodynamics. The microscopic origin of condensation and phase separations

Abstract

Conventional thermo-statistics address infinite homogeneous systems within the canonical ensemble. However, some 150 years ago the original motivation of thermodynamics was the description of steam engines, i.e. boiling water. Its essential physics is the separation of the gas phase from the liquid. Of course, boiling water is inhomogeneous and as such cannot be treated by canonical thermo-statistics. Then it is not astonishing, that a phase transition of first order is signaled canonically by a Yang-Lee singularity. Thus it is only treated correctly by microcanonical Boltzmann-Planck statistics. This is elaborated in the present article. It turns out that the Boltzmann-Planck statistics is much richer and gives fundamental insight into statistical mechanics and especially into entropy. This can even be done to some extend rigorously and analytically. The microcanonical entropy has a very simple physical meaning: It measures the microscopic uncertainty that we have about the system, i.e. the number of points in $6N$-dim phase, which are consistent with our information about the system. It can rigorously be split into an ideal-gas part and a configuration part which contains all the physics and especially is responsible for all phase transitions. The deep and essential difference between ``extensive'' and ``intensive'' control parameters, i.e. microcanonical and canonical statistics, is exemplified by rotating, self-gravitating systems.

Invited paper for the conference "Frontiers of Quantum and Mesoscopic Thermodynamics", Prague 26-29 July 2004, 9 pages, 3 figures A detailed discussion of Clausius original papers on entropy are added

References in corpus (6)

• Microcanonical mean-field thermodynamics of self-gravitating and rotating systems
• Statistical mechanics and phase diagrams of rotating self-gravitating fermions
• Negative heat capacities and first order phase transitions in nuclei
• A New Thermodynamics from Nuclei to Stars III
• Comment on "Negative heat capacities and first order phase transitions in nuclei" by L.G. Moretto et al
• Comment on "Negative heat and first order phase transitions in nuclei" by Moretto et al

Cited by in corpus (4)

• Simulated Dark-Matter Halos as a Test of Nonextensive Statistical Mechanics
• Thermodynamics of Peptide Aggregation Processes. An Analysis from Perspectives of Three Statistical Ensembles
• Entropy and the Typicality of Universes
• Caloric curve for nuclear liquid-gas phase transition in relativistic mean-field hadronic model