In this paper, we calculate the soft-collisional energy loss of heavy quarks traversing the viscous quark-gluon plasma including the effects of a finite relaxation time $tau_pi$ on the energy loss. We find that the collisional energy loss depends app
reciably on $tau_pi$ . In particular, for typical values of the viscosity-to-entropy ratio, we show that the energy loss obtained using $tau_pi$ = 0 can be $sim$ 10$%$ larger than the one obtained using $tau_pi$ = 0. Moreover, we find that the energy loss obtained using the kinetic theory expression for $tau_pi$ is much larger that the one obtained with the $tau_pi$ derived from the Anti de Sitter/Conformal Field Theory correspondence. Our results may be relevant in the modeling of heavy quark evolution through the quark-gluon plasma.
We show that the usual linear analysis of QGP Weibel instabilities based on the Maxwell-Boltzmann equation may be reproduced in a purely hydrodynamic model. The latter is derived by the Entropy Production Variational Method from a transport equation
including collisions, and can describe highly nonequilibrium flow. We find that, as expected, collisions slow down the growth of Weibel instabilities. Finally, we discuss the strong momentum anisotropy limit.
We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear closure suggest
ed by the Entropy Production Principle; the evolution equation is obtained by the method of moments, and together with energy-momentum conservation closes the system. Transport coefficients are chosen to reproduce second order fluid dynamics if gradients are small. We compare the resulting formalism to exact solutions of Boltzmanns equation in 0+1 dimensions and show that it tracks kinetic theory better than second order fluid dynamics.
Starting from kinetic theory, we obtain a nonlinear dissipative formalism describing the nonequilibrium evolution of scalar colored particles coupled selfconsistently to nonabelian classical gauge fields. The link between the one-particle distributio
n function of the kinetic description and the variables of the effective theory is determined by extremizing the entropy production. This method does not rely on the usual gradient expansion in fluid dynamic variables, and therefore the resulting effective theory can handle situations where these gradients (and hence the momentum-space anisotropies) are expected to be large. The formalism presented here, being computationally less demanding than kinetic theory, may be useful as a simplified model of the dynamics of color fields during the early stages of heavy ion collisions and in phenomena related to parton energy loss.
Within the framework of relativistic fluctuating hydrodynamics we compute the contribution of thermal fluctuations to the effective infrared shear viscosity of a conformal fluid, focusing on quadratic (in fluctuations), second order (in velocity grad
ients) terms in the conservation equations. Our approach is based on the separation of hydrodynamic fields in soft and ultrasoft sectors, in which the effective shear viscosity arises due to the action of the soft modes on the evolution of the ultrasoft ones. We find that for a strongly coupled fluid with small shear viscosity--to--entropy ratio $eta/s$ the contribution of thermal fluctuations to the effective shear viscosity is small but significant. Using realistic estimates for the strongly coupled quark--gluon plasma created in heavy ion collisions, we find that for $eta/s$ close to the AdS/CFT lower bound $1/(4pi)$ the correction is positive and at most amounts to 10% in the temperature range 200--300 MeV, whereas for larger values $eta/s sim 2/(4pi)$ the correction is negligible. For weakly coupled theories the correction is very small even for $eta/s=0.08$ and can be neglected.
