$$C_V=\frac{3}{2}k_B+
Nk_B\beta^2\left(\langle E_P^2\rangle - \langle E_P\rangle^2\right)
\label{eq:sphtFluct}$$ In equilibrium these two ways of calculating the specific heat should agree. So we compare the results of calculating $C_V$ both ways as a check on our calculation and to make sure the system has equilibrated in all the basins that were visited in the energy landscape.

Specific Heat Versus Temperature
--------------------------------

The specific heat at constant volume exhibits a peak at the glass transition as shown in Figure \[fig:sphtFluctdEdT\]. The data in this figure is for 512 particles and was averaged over 6 runs with a measurement time of $3\times 10^6$ md steps. Notice that there is good agreement between calculating the specific heat by taking a derivative of the energy with respect to temperature (see eq. (\[eq:sphtDeriv\])) and by using fluctuations (see eq. (\[eq:sphtFluct\])). This implies that the system has equilibrated within the basins that it visits in the energy landscape. We find similar agreement for other run times. At low temperatures the specific heat goes to 3$k_B$ as expected for classical oscillators while at high temperatures $C_V$ approaches $3k_B/2$ which corresponds to an ideal gas.

[Fig3.eps]{}

The peak in the specific heat occurs at $T\approx 0.3$ which corresponds to $\Gamma\approx 