Lorentzian Entropies and Olbert's κ - Distribution

Treumann, Rudolf A. and Baumjohann, Wolfgang (21. July 2020): Lorentzian Entropies and Olbert's κ - Distribution. In: Frontiers in Physics, Vol. 8, 221: pp. 1-9

Abstract

This note derives the various forms of entropy of a systems subject to Olbert distributions (generalized Lorentzian probability distributions known as kappa-distributions), which are frequently observed, particularly in high-temperature plasmas. The general expression of the partition function in such systems is given as well in a form similar to the Boltzmann-Gibbs probability distribution, including a possible exponential high-energy truncation. We find the representation of the mean energy as a function of probability, and we provide the implicit form of Olbert (Lorentzian) entropy as well as its high-temperature limit. The relation to phase space density of states is obtained. We then find the entropy as a function of probability, an expression that is fundamental to statistical mechanics and, here, to its Olbertian version. Lorentzian systems through internal collective interactions cause correlations that add to the entropy. Fermi systems do not obey Olbert statistics, while Bose systems might do so at temperatures that are sufficiently far from zero.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Keywords: Generalized entropy; Lorentzian systems; Lorentzian countings; Olbert distribution; κ distribution
• Faculties: Geosciences > Department of Earth and Environmental Sciences
• Subjects: 500 Science > 550 Earth sciences and geology
• ISSN: 2296-424X
• Language: English