  A computation of the quotient of shear viscosity to entropy density, or KSS
number $\eta/s$ is performed, in the non-relativistic and classical regime,
first in Chiral Perturbation Theory, and then in the $SO(g+1)/SO(g)$ Non-Linear
Sigma Model in the large $g$ limit. Both are field theories stemming from a
renormalizable Sigma Model but in spite of that, we explicitly calculate how
one undercomes the KSS bound by increasing the number of degenerate pions
sufficiently. However we argue that particle production could still keep the
validity of the KSS bound in the weak sense. We also show how a large number of
molecular isomers (that we estimate in terms of simple molecular properties)
could undercome the bound in the strong sense. This might be possible with
carbon-based molecules. We finally argue that a measurement of $\eta/s$ in
Heavy Ion Collisions might be turned into an upper bound on the number of
hadron resonances.
