eta/s is critical (at phase transitions)

The viscosity over entropy density ratio, or KSS number, can help isolate the critical point in the hadron phase-diagram in Relativistic Heavy Ion Collisions. We argue that this quantity does have a minimum at a phase transition or crossover. Although indications from conventional non-relativistic gases point out to even a divergence in eta/s when the phase-transition is first-order, since the critical exponent is rather low, this will be more difficult to ascertain in RHIC or FAIR. The experimental data are more likely to reveal a discontinuity for a first order phase transition or a smooth minimum at a crossover.