Nonextensive hydrodynamics of boost-invariant plasmas

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 → 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.

Constraining the initial stages of ultrarelativistic nuclear collisions

“…The qualitative picture seen in Fig. 4 is typical of Bjorken flow in many models of equilibration, including various extensions of MIS theory, anisotropic hydrodynamics [76,77], kinetic theory as well as strongly coupled N = 4 SYM theory. Before reviewing some of them, we will try to understand the features seen in this plot in a quantitative way, using asymptotic methods to extract the relevant physics from Eq.…”

Initial state and approach to equilibrium

“…Far-from-equilibrium attractors are a typical feature of conformal Bjorken flow also in more general hydrodynamic models [6,7]. Such models are constructed to reproduce the asymptotics of microscopic theories near equilibrium; their solutions coincide only in the late time asymptotic region (see e.g.…”