Nonextensive hydrodynamics of boost-invariant plasmas

TL;DR

This paper develops a nonextensive hydrodynamic model using Tsallis statistics to study boost-invariant plasmas, revealing that early-time bulk pressure evolution is sensitive to nonextensivity, while other observables are less affected.

Contribution

It introduces a dynamical framework for nonextensive hydrodynamics with a time-dependent nonextensivity parameter, extending quasiparticle anisotropic hydrodynamics to include Tsallis statistics.

Findings

Early-time bulk pressure evolution differs significantly with nonextensivity.

Temperature and energy density evolution are insensitive to the distribution function.

Existence of non-conformal hydrodynamic attractors for pressures and viscous corrections.

Abstract

We use quasiparticle anisotropic hydrodynamics to study the non-conformal and non-extensive dynamics of a system undergoing boost-invariant Bjorken expansion. To introduce nonextensivity, we use an underlying Tsallis distribution with a time-dependent nonextensivity parameter $q$. By taking moments of the quasiparticle Boltzmann equation in the relaxation-time approximation, we obtain dynamical equations which allow us to determine the time evolution of all microscopic parameters including $q$. We compare numerical solutions for bulk observables obtained using the nonextensive evolution with results obtained using quasiparticle anisotropic hydrodynamics with a Boltzmann distribution function ($q \rightarrow 1$). We show that the evolution of the temperature, pressure ratio, and scaled energy density, are quite insensitive to which distribution function is assumed. However, we find significant differences in the early-time evolution of the bulk pressure which are observed for even small deviations from the Boltzmann distribution function. Finally, we discuss the existence of non-conformal hydrodynamic attractors for the longitudinal and transverse pressures, the bulk and shear viscous corrections, and the nonextensivity parameter $q$.