1. Generalized Entropy and Transport Coefficients of Hadronic Matter Azwinndini Muronga 1,2 1 Centre for Theoretical Physics & Astrophysics Department of Physics, University of Cape Town 2 UCT-CERN Research Centre Department of Physics, University of Cape Town Zimanyi 75 Memorial Workshop 02-04 July 2007, Budapest, Hungary

2. Transport properties of relativistic nuclear matter Viscosities, diffusivities, conductivities. Determine relaxation to equilibrium in heavy ion collisions – chemical equilibration (by flavor, spin and color diffusion) In astrophysical situations such as in neutron stars – cooling and burning of neutron star into a strange quark star In cosmological applications such as the early universe – electroweak baryogenesis QED and QCD plasmas Complete fluid dynamics solution requires - initial conditions - equation of state - transport coefficients Extract the transport coefficients and associated time/length scales for a given model of interacting hadrons and/or partons. Study the sensitivity of the space-time evolution of the system and the calculated distribution of the hadrons to dissipative, non- equilibrium processes Compare the predicted distribution with those observed in experiments Baym et. al.; Gavin, Prakash et. al.; Davesne; Heiselberg, Muroya et. al.; Arnold et. al.; AM; Z. Xu and C. Greiner

4. Origin of the news:

6. The interest in shear viscosity to entropy ratio Energy equation EoS and Transport coefficients Temperature evolution AM, 2002; 2004

7. Time evolution of thermodynamic quantities

8. Generalized entropy 4-current Entropy 4-current: Muller-Israel-Stewart Entropy density and entropy flux Entropy production See AM, nuc-th/0611090 for details

9. Relaxation equations for dissipative fluxes Relaxation equations for the dissipative fluxes Relaxation times/lengths

10. Fluctuations and Transport Coefficients Green-Kubo From generalized entropy

11. Transport Coefficients and Equation of State From Maxwell-Cattaneo-type equations Thermodynamics from transport models Thermodynamics from hadronic gas model (e.g. mesons)

12. Relaxation Coefficients

13. Shear viscosity and shear relaxation time AM, 2004; See also, A. El, C. Greiner and Z. Xu, hep-ph 0706412, using parton model

14. Transport coefficients are as important as the equation of state. Transport coefficients and relaxation times/lengths probe different time/length scales in fluid dynamics (physics of many scales) They should be calculated/extracted self consistently together with the equation of state. The relaxation times/lengths should be compared with the characteristic time/length scales of the system under consideration. Knowledge of transport coefficients and associated length/time scales provides good ground for comparison of theoretical prediction with experiments Looking beyond the perfect picture