  We describe a new paradox for ideal fluids. It arises in the accretion of an
\textit{ideal} fluid onto a black hole, where, under suitable boundary
conditions, the flow can violate the generalized second law of thermodynamics.
The paradox indicates that there is in fact a lower bound to the correlation
length of any \textit{real} fluid, the value of which is determined by the
thermodynamic properties of that fluid. We observe that the universal bound on
entropy, itself suggested by the generalized second law, puts a lower bound on
the correlation length of any fluid in terms of its specific entropy. With the
help of a new, efficient estimate for the viscosity of liquids, we argue that
this also means that viscosity is bounded from below in a way reminiscent of
the conjectured Kovtun-Son-Starinets lower bound on the ratio of viscosity to
entropy density. We conclude that much light may be shed on the
Kovtun-Son-Starinets bound by suitable arguments based on the generalized
second law.
