  We consider the homogeneous and isotropic cosmological fluid dynamics which
is compatible with a homothetic, timelike motion, equivalent to an equation of
state $\rho + 3P = 0$. By splitting the total pressure $P$ into the sum of an
equilibrium part $p$ and a non-equilibrium part $\Pi$, we find that on
thermodynamical grounds this split is necessarily given by $p = \rho$ and $\Pi
= - (4/3)\rho$, corresponding to a dissipative stiff (Zel'dovich) fluid.
