Thermodynamic Derivation of the Tsallis and R\'enyi Entropy Formulas and the Temperature of Quark-Gluon Plasma

TL;DR

This paper derives Tsallis and Rényi entropy formulas from thermodynamic principles, relates the parameters to physical properties of a reservoir, and applies the framework to determine the temperature of quark-gluon plasma in high-energy collisions.

Contribution

It provides a thermodynamic derivation of Tsallis and Rényi entropies and links their parameters to reservoir properties, with applications to quark-gluon plasma temperature estimation.

Findings

Derived Tsallis entropy from thermostat independence.

Expressed subsystem temperature and entropy index in terms of reservoir properties.

Applied the framework to analyze hadron spectra and determine quark-gluon plasma temperature.

Abstract

We derive Tsallis entropy, Sq, from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result for finite thermostats interprets thermodynamically the subsystem temperature, T1, and the index q in terms of the temperature, T, entropy, S, and heat capacity, C of the reservoir as T1 = T exp(-S/C) and q = 1 - 1/C. In the infinite C limit, irrespective to the value of S, the Boltzmann-Gibbs approach is fully recovered. We apply this framework for the experimental determination of the original temperature of a finite thermostat, T, from the analysis of hadron spectra produced in high energy collisions, by analyzing frequently considered simple models of the quark-gluon plasma.