the specific heat exhibits a smooth step down as the temperature is lowered through the glass transition. In our simulations which are done at constant volume, the specific heat has a peak at the glass transition. It is a useful check of our calculation to see if the peak occurs at the same temperature (or density) as the drop in the linear generalized compressibility. There are two ways to compute the specific heat $C_V$ per particle at constant volume $V$. The first is by taking a derivative of the average energy $\langle E\rangle$ per particle with respect to temperature: $C_V=d\langle E\rangle/dT$. Since we study the system at discrete temperatures, we approximate the derivative by a finite difference: $$C_V(T_n)=\frac{\langle E(T_n)\rangle -\langle E(T_{n-1})\rangle}{T_n-T_{n-1}}
\label{eq:sphtDeriv}$$ where $T_n>T_{n-1}$ for all integers $n$. The second way to calculate the specific heat is from the fluctuations: $$C_V=N k_B\beta^2\left(\langle E_P^2\rangle - \langle E_P\rangle^2\right)$$ where $k_B$ is Boltzmann’s constant, $\beta$ is the inverse temperature, and $E_P$ is the potential energy per particle. In our three dimensional simulations the kinetic energy per particle is given by $3k_BT/2$, so it is the fluctuations in the potential energy $E_P$ per particle which determine the temperature dependence of the specific heat. Thus 