Nonequilibrium entropy density and dissipative processes in relativistic

Non-equilibrium entropy density and dissipative processes in relativistic nuclear collisions Azwinndini Muronga 1, 2 Centre for Theoretical Physics and Astrophysics Department of Physics, University of Cape Town, South Africa 2 UCT-CERN Research Centre Department of Physics, University of Cape Town, South Africa Quark Matter 2008 20 th International Conference on Ultra-Relativistic Nucleus Collisions (QM 2008) February 4 -10, 2008 : Jaipur, India 1

References • Recall talks by A. K. Chaudhuri, Xu Zhe, S. Gavin, A. El, T. Hirano, D. Molnar, R. Bhalerao, U. Heinz • See also talks by T. Csorgo, T. Kodama, P. Bozek, K. Itakura

Entropy 4 -current, density and flux Entropy 4 -current Entropy density Entropy flux Second Law of thermodynamics The 3 new coefficients in the entropy density are related to the relaxation times and are responsible for causality while the 2 new coefficients in the entropy flux are related to the relaxation length and are responsible for the coupling between heat flow and viscous stresses

Relaxation equations for dissipative fluxes Relaxation equations for the dissipative fluxes Transport and relaxation times/lengths

Relaxation Coefficients

Entropy density and entropy production Entropy density Entropy production Relevant ratios

Shear viscosity in the scaling solution Energy equation Reynold’s number vs eta/s

Numerical and Conceptual Questions for Dissipative Relativistic Fluid Dynamics q q q What is the underlying theory? What are the initial conditions? What are the boundary conditions? What is the underlying equation of state? What are the transport coefficients? Which numerical algorithm is implemented? q Which tests are caried out? q Numerical viscosity? q What are the additional parameters? q How is the freeze out implemented?

η/s=1/4π gives you a “perfect” picture • All processes that contribute to the entropy production should be studied • Initial conditions, equation of state and transport coefficients should be studied selfconsistently • Numerical schemes should be tested against analytical solutions • The study of entropy evolution is important in constraining the IC, EOS, and TC.