Abstract
In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics, and neutron stars. We review some recent investigations on the power-law distributions arising in high energy physics experiments focusing on a thermodynamic description of the system formed, which could explain the power-law behavior. The possible connections with a fractal structure of hadrons is also discussed. The main objective of the present work is to delineate the state-of-the-art of those studies and show some open issues that deserve more careful investigation. We propose several possibilities to test the theory through analyses of experimental data.
Highlights
An interesting description of hadronic systems in the hot and in the dense regimes, known as quark-gluon plasma (QGP), has been developed in recent years
We show how the thermodynamic aspects of the Yang–Mills fields reflect the fractal structure in a way similar to the thermofractals, which were introduced to show how Tsallis statistics can emerge in thermodynamic systems, and study its main thermodynamic quantities
Extend to other aspects, as the power-law behavior of the high energy collisions (HEC) distribution, which are described by Tsallis statistics and allow to access experimentally the value of the entropic index, q, that results to be in very good agreement with the value found by the theory
Summary
An interesting description of hadronic systems in the hot and in the dense regimes, known as quark-gluon plasma (QGP), has been developed in recent years. Motivated by the large amount of information that emerged from high energy physics (HEP) experiments, the consequences of those advances are far-reaching, since they may be present in any Yang–Mills field (YMF) theory. We will give a short review of those developments, discuss the experimental evidence of the new theoretical approach, and present some applications to HEP, hadron physics, and astrophysics. Before entering in the main subject of this work, let us summarize the three fundamental theories that form the foundations for the developments that will be discussed below. These three theories are: the YMF; the fractal geometry; and the non-extensive statistics proposed by Constantino Tsallis.
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