Shear-viscosity to entropy-density ratio of a relativistic hadron gas.

Ultrarelativistic heavy-ion collisions at the Brookhaven National Laboratory Relativistic Heavy Ion Collider (RHIC) are thought to have produced a state of matter called the quark-gluon plasma, characterized by a very small shear-viscosity to entropy-density ratio eta/s, near the lower bound predicted for that quantity by anti-de Sitter space/conformal field theory methods. As the produced matter expands and cools, it evolves through a phase described by a hadron gas with rapidly increasing eta/s. We calculate eta/s as a function of temperature in this phase both in and out of chemical equilibrium and find that its value poses a challenge for viscous relativistic hydrodynamics, which requires small values of eta/s in order to successfully describe the collective flow observables at the RHIC.