Fractal Structures of Yang-Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics

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.