  We define and compute the (analogue) shear viscosity to entropy density ratio
$\tilde\eta/s$ for the QFTs dual to spherical AdS black holes both in Einstein
and Gauss-Bonnet gravity in five spacetime dimensions. Although in this case,
owing to the lack of translational symmetry of the background, $\tilde\eta$
does not have the usual hydrodynamic meaning, it can be still interpreted as
the rate of entropy production due to a strain. At large and small
temperatures, it is found that $\tilde\eta/s$ is a monotonic increasing
function of the temperature. In particular, at large temperatures it approaches
a constant value, whereas, at small temperatures, when the black hole has a
regular, stable extremal limit, $\tilde\eta/s$ goes to zero with scaling law
behaviour. Whenever the phase diagram of the black hole has a Van der
Waals-like behaviour, i.e. it is characterised by the presence of two stable
states (small and large black holes) connected by a meta-stable region
(intermediate black holes), the system evolution must occur through the
meta-stable region and temperature-dependent hysteresis of $\tilde\eta/s$ is
generated by non-equilibrium thermodynamics.
