  Using Taylor expansions of the pressure obtained previously in studies of
2-flavor QCD at non-zero chemical potential we calculate expansion coefficients
for the energy and entropy densities up to ${\cal O}(\mu_q^6)$ in the quark
chemical potential. We use these series in $\mu_q/T$ to determine lines of
constant entropy per baryon number ($S/N_B$) that characterize the expansion of
dense matter created in heavy ion collisions. In the high temperature regime
these lines are found to be well approximated by lines of constant $\mu_q/T$.
In the low temperature phase, however, the quark chemical potential is found to
increase with decreasing temperature. This is in accordance with resonance gas
model calculations. Along the lines of constant $S/N_B$ we calculate the energy
density and pressure. Within the accuracy of our present analysis we find that
the ratio $p/\epsilon$ for $T>T_0$ as well as the softest point of the equation
of state, $(p/\epsilon)_{min}\simeq 0.075$, show no significant dependence on
$S/N_B$.
