Nonextensive statistical mechanics - Applications to nuclear and high energy physics

TL;DR

This paper reviews nonextensive statistical mechanics, highlighting its applications in nuclear and high energy physics where traditional Boltzmann-Gibbs theory fails, emphasizing power-law behaviors and recent theoretical developments.

Contribution

It provides a comprehensive overview of nonextensive statistical mechanics and its applications in various high-energy physics phenomena, including recent generalizations of the theory.

Findings

Systems follow power-law distributions instead of exponential ones.

Nonextensive mechanics explains phenomena like cosmic rays and quark-gluon plasma.

Recent theoretical developments extend the framework of nonextensive statistics.

Abstract

A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the system appears to relax, along time, on macroscopic states which violate the ergodic assumption. Some of these phenomena appear to follow, instead, the prescriptions of nonextensive statistical mechanics. In the same manner that the BG formalism is based on the entropy $S_{BG}=-k \sum_i p_i \ln p_i$, the nonextensive one is based on the form $S_q=k(1-\sum_ip_i^q)/(q-1)$ (with $S_1=S_{BG}$). Typically, the systems following the rules derived from the former exhibit an {\it exponential} relaxation with time toward a stationary state characterized by an {\it exponential} dependence on the energy ({\it thermal equilibrium}), whereas those following the rules derived from the latter are characterized by (asymptotic) {\it power-laws} (both the typical time dependences, and the energy distribution at the stationary state). A brief review of this theory is given here, as well as of some of its applications, such as electron-positron annihilation producing hadronic jets, collisions involving heavy nuclei, the solar neutrino problem, anomalous diffusion of a quark in a quark-gluon plasma, and flux of cosmic rays on Earth. In addition to these points, very recent developments generalizing nonextensive statistical mechanics itself are mentioned.