Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect

This paper develops explicit and consistent definitions of the independent thermodynamic properties of temperature and the kappa index within the framework of nonextensive statistical mechanics and shows their connection with the formalism of kappa distributions. By defining the “entropy defect” in the composition of a system, we show how the nonextensive entropy of systems with correlations differs from the sum of the entropies of their constituents of these systems. A system is composed extensively when its elementary subsystems are independent, interacting with no correlations; this leads to an extensive system entropy, which is simply the sum of the subsystem entropies. In contrast, a system is composed nonextensively when its elementary subsystems are connected through long-range interactions that produce correlations. This leads to an entropy defect that quantifies the missing entropy, analogous to the mass defect that quantifies the mass (energy) associated with assembling subatomic particles. We develop thermodynamic definitions of kappa and temperature that connect with the corresponding kinetic definitions originated from kappa distributions. Finally, we show that the entropy of a system, composed by a number of subsystems with correlations, is determined using both discrete and continuous descriptions, and find: (i) the resulted entropic form expressed in terms of thermodynamic parameters; (ii) an optimal relationship between kappa and temperature; and (iii) the correlation coefficient to be inversely proportional to the temperature logarithm.

Statefinder diagnosis for Tsallis agegraphic dark energy model with ωD − ωD′ pair

A new class of dark energy model, known as “Tsallis agegraphic dark energy (TADE),” has been proposed using the holographic principle and Tsallis nonextensive entropy (Mod. Phys. Lett. A, 2019), considering the conformal time as well as the age of the Universe as IR cutoffs in flat Universe. The trajectories for evolution of statefinder parameters in [Formula: see text], [Formula: see text], [Formula: see text] and the [Formula: see text] planes are plotted for the TADE 1 and TADE 2 models for the value of the Tsallis parameter [Formula: see text], and taking the TADE energy density parameter [Formula: see text], according to the Planck 2018 results VI — [Formula: see text]CDM observational data without interaction.

Tsallis nonextensive entropy and the multiplicity distributions in high energy leptonic collisions

The nonextensive behavior of entropy is exploited to explain the regularity in multiplicity distributions in [Formula: see text] collisions at high energies. The experimental data are analyzed by using Tsallis [Formula: see text]-statistics. We propose a new approach of applying Tsallis [Formula: see text]-statistics, wherein the multiplicity distribution is divided into two components; two-jet and multijet components. A convoluted Tsallis distribution is fitted to the data. It is shown that this method gives the best fits which are several orders better than the conventional fit of Tsallis distribution.