Entropy production in high-energy heavy-ion collisions and the correlation of shear viscosity and thermalization time

Abstract

We study entropy production in the early stage of high-energy heavy-ion collisions due to shear viscosity. We employ the second-order theory of Israel-Stewart with two different stress relaxation times, as appropriate for strong coupling or for a Boltzmann gas, respectively, and compare the hydrodynamic evolution. Based on present knowledge of initial particle production, we argue that entropy production is tightly constrained. We derive new limits on the shear viscosity to entropy density ratio η/s, independent from elliptic flow effects, and determine the corresponding Reynolds number. Furthermore, we show that for a given entropy production bound, that the initial time τ0 for hydrodynamics is correlated to the viscosity. The conjectured lower bound for η/s provides a lower limit for τ0.

Bulk viscosity-driven suppression of shear viscosity effects on the flow harmonics at energies available at the BNL Relativistic Heavy Ion Collider

“…Moreover, as discussed in [50], constraints on the entropy production generate a correlation between the values of transport coefficients and the initial time for hydrodynamics. If bulk viscosity effects compensate the effects from shear, η/s could be larger than used here and, consequently, τ 0 may actually be larger than usually considered in hydrodynamic simulations.…”

Nonextensive perfect hydrodynamics — a model of dissipative relativistic hydrodynamics?

“…However, one needs their special relativistic generalization and this turns out to be acausal and unstable [64,65] (see also [66][67][68][69][70][71]). One therefore looks towards the extended, second order theories accepting all problems connected with their formulation and practical applications [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87]. Physically, the difference is that first order theories are based on the local equilibrium hypothesis, in which independent variables are used, whereas in higher order theories only the fluxes of the local equilibrium theory appear as independent variables.…”

“…One can see that it has form of a dissipative hydrodynamic equation [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87] is the shear (symmetric and traceless) pressure tensor. They are defined as (using the angular bracket notation:…”

Aspects of causal viscous hydrodynamics

“…Finally, we note that the maximum entropy production occurs in the very early stages of the flow, and probes of this stage of the expansion would best discriminate between different values of τ π . A different approach to extracting τ π is advocated in [17].…”

“…Such a claim must be substantiated by a study of viscous fluid dynamics. Until now there have been very few studies of non-ideal fluids in this context [9,10,11,12,13,14,15,16,17].…”