  Linear irreversible thermodynamics asserts that the instantaneous local
spontaneous entropy production is always nonnegative. However for a
viscoelastic fluid this is not always the case. Given the fundamental status of
the Second Law, this presents a problem. We provide a new derivation of the
Second Law, from first principles, which is valid for the appropriately time
averaged entropy production allowing the instantaneous entropy production to be
negative for short intervals of time. We show that time averages (rather than
instantaneous values) of the entropy production are nonnegative. We illustrate
this using molecular dynamics simulations of oscillatory shear.
