  We determine analytically the dependence of the approach to thermal
equilibrium of strongly coupled plasmas on the breaking of scale invariance.
The theories we consider are the holographic duals to Einstein gravity coupled
to a scalar with an exponential potential. The coefficient in the exponent,
$X$, is the parameter that controls the deviation from the conformally
invariant case. For these models we obtain analytic solutions for the plasma
expansion in the late-time limit, under the assumption of boost-invariance, and
we determine the scaling behaviour of the energy density, pressure, and
temperature as a function of time. We find that the temperature decays as a
function of proper time as $T\sim \tau^{-s/4}$ with $s$ determined in terms of
the non-conformality parameter $X$ as $s=4(1-4X^2)/3$. This agrees with the
result of Janik and Peschanski, $s=4/3$, for the conformal plasmas and
generalizes it to non-conformal plasmas with $X\neq 0$. We also consider more
realistic potentials where the exponential is supplemented by power-law terms.
Even though in this case we cannot have exact solutions, we are able under
certain assumptions to determine the scaling of the energy, that receives
logarithmic corrections.
