Speaker
Description
This talk provides an in-depth analysis of the emergence of Tsallis Statistics through fractal structures in high-energy collisions in the context of high-energy physics and hadron physics. The self-similarity in the parton structure resulting from the scale properties of the Callan-Symanzik Equation is examined, demonstrating the recursive relations that allow for the emergence of Tsallis distributions. The implications of these results, including the relation between the Tsallis parameter q and the number of colours and flavours, are discussed in detail.
Moreover, both theoretical and experimental studies supporting the emergence of Tsallis
distributions in high-energy collisions, including studies on heavy-ion collisions and proton-proton collisions, are presented. The talk also explores the potential applications of non-extensive statistical mechanics in addressing longstanding problems in traditional statistical mechanics, such as non-equilibrium phenomena, anomalous diffusion, and non-Gaussian fluctuations.
Furthermore, the derivation of the Plastino-Plastino Equation from the Boltzmann Equation for systems with non-local correlations using q-calculus is presented. The solutions of this equation are compared to those of the Fokker-Planck Equation, and possible connections between q-calculus with fractal and fractional derivatives are explored. The q-calculus derivative is shown to be a continuous approximation of the Parvate-Gangal fractal derivative, and the Caputo’s fractional derivative can be obtained from the q-calculus derivative as a non-local continuous approximation of the fractal derivative.
Finally, the talk discusses the potential extension of the same theoretical approach for the study of hadron structure, in view of the z-scaling connections with the Tsallis distributions and with thermofractal structure. This comprehensive analysis provides valuable insights into the intricate relationship between fractal structures, Tsallis Statistics, and non-local correlations in high-energy collisions, highlighting their significance for the field of high-energy physics and hadron physics.
