Nonextensive critical effects in relativistic nuclear mean field models

TL;DR

This paper extends relativistic nuclear mean field models by incorporating nonextensive statistical effects via Tsallis entropy, analyzing how these modifications influence the behavior of strongly interacting matter near critical points.

Contribution

It introduces a nonextensive version of the NJL model to account for environmental fluctuations in nuclear matter, expanding the modeling framework beyond traditional BG statistics.

Findings

Model sensitivity to nonextensivity parameter q near critical points

Nonextensive effects influence the phase behavior of strongly interacting matter

Potential implications for understanding fluctuations in nuclear environments

Abstract

We present a possible extension of the usual relativistic nuclear mean field models widely used to describe nuclear matter towards accounting for the influence of possible intrinsic fluctuations caused by the environment. Rather than individually identifying their particular causes we concentrate on the fact that such effects can be summarily incorporated in the changing of the statistical background used, from the usual (extensive) Boltzman-Gibbs one to the nonextensive taken in the form proposed by Tsallis with a dimensionless nonextensivity parameter $q$ responsible for the above mentioned effects (for $q \rightarrow 1$ one recovers the usual BG case). We illustrate this proposition on the example of the QCD-based Nambu - Jona-Lasinio (NJL) model of a many-body field theory describing the behavior of strongly interacting matter presenting its nonextensive version. We check the sensitivity of the usual NJL model to a departure from the BG scenario expressed by the value of $| q - 1|$, in particular in the vicinity of critical points.