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# Entropy production for an interacting quark-gluon plasma

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### Abstract

We investigate the entropy production within dissipative hydrodynamics in the Israel-Stewart (IS) and Navier-Stokes theory (NS) for relativistic heavy ion physics applications. In particular we focus on the initial condition in a 0+1D Bjorken scenario, appropriate for the early longitudinal expansion stage of the collision. Going beyond the standard simplification of a massless ideal gas we consider a realistic equation of state consistently derived within a virial expansion. The EoS used is well in line with recent three-flavor QCD lattice data for the pressure, speed of sound, and interaction measure at nonzero temperature and vanishing chemical potential ($$\mu_{\rm q} = 0$$). The shear viscosity has been consistently calculated within this formalism using a kinetic approach in the ultra-relativistic regime with an explicit and systematic evaluation of the transport cross section as function of temperature. We investigate the influence of the viscosity and the initial condition, i.e. formation time, initial temperature, and pressure anisotropy for the entropy production at RHIC at $$\sqrt{s_{\rm NN}}=130$$ GeV. We find that the interplay between effects of the viscosity and of the realistic EoS can not be neglected in the reconstruction of the initial state from experimental data. Therefore, from the experimental findings it is very hard to derive unambiguous information about the initial conditions and/or the evolution of the system.

### Most cited references26

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### The Nambu—Jona-Lasinio model of quantum chromodynamics

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### Diquark Bose Condensates in High Density Matter and Instantons

(1997)
Instantons lead to strong correlations between up and down quarks with spin zero and anti-symmetric color wave functions. In cold and dense matter, $$n_b>n_c\simeq 1 fm^{-3}$$ and $$T$$ condensate and restoring chiral symmetry. At high density, the ground state is a color superconductor in which diquarks play the role of Cooper pairs. An interesting toy model is provided by QCD with two colors: it has a particle-anti-particle symmetry which relates  and  condensates.
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### Phases of QCD: lattice thermodynamics and a field theoretical model

(2005)
We investigate three-colour QCD thermodynamics at finite quark chemical potential. Lattice QCD results are compared with a generalized Nambu Jona-Lasinio model in which quarks couple simultaneously to the chiral condensate and to a background temporal gauge field representing Polyakov loop dynamics. This so-called PNJL model thus includes features of both deconfinement and chiral symmetry restoration. The parameters of the Polyakov loop effective potential are fixed in the pure gauge sector. The chiral condensate and the Polyakov loop as functions of temperature and quark chemical potential are calculated by minimizing the thermodynamic potential of the system. The resulting equation of state, (scaled) pressure difference and quark number density at finite quark chemical potential are then confronted with corresponding Lattice QCD data.
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### Author and article information

###### Journal
17 May 2011
###### Article
10.1016/j.nuclphysa.2012.09.003
1105.3357

26 pages, 4 figures, 2 tables
hep-ph