We point out that in the early universe, for temperatures in the approximate interval 175-80 MeV (after the quark-gluon plasma), pions carried a large share of the entropy and supported the largest inhomogeneities. Thus, we examine the production of
entropy in a pion gas, particularizing to inhomogeneities of the temperature, for which we benefit from the known thermal conductivity. We finally put that entropy produced in relaxing such thermal inhomogeneities in the broad context of this relatively unexplored phase of early-universe cosmology.
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. Althoug
h 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.
In this work we briefly review the Kovtun-Son-Starinet (KSS) computation of the ratio eta/s for quantum field theories with gravitational dual and the related conjecture that it is bound from below by 1/(4 pi). We discuss the validity of the bound an
d the nature of its possible violations, its relevance for RHIC, its connection with phase transitions and other related issues.
