any further. We can recast eq. (\[eq:expansion\]) as a power series in the perturbation $\Delta P$: $$\label{eq:DV2}
{\delta\rho_{\phi} \over {N}}=
-{1\over 6\rho_o k_B T}\chi_{l}\Delta P+{1\over 6(\rho_o k_B T)^3}\chi_{nl}
(\Delta P)^3$$ where $$\chi_{l}={6 \over N}\langle (\rho_{\phi})^2\rangle_c \quad\;\;\;\;
\chi_{nl}=-{ 1 \over N}\langle (\rho_{\phi})^4\rangle_c.
\label{eq:susceptibilities}$$ In this paper we will focus our attention on the linear ($\chi_{l}$) and nonlinear ($\chi_{nl}$) dimensionless generalized compressibilities defined by the above expressions.

We now discuss the choice of the function $\phi$. We consider applying the potential along the direction $\mu$ of one of the coordinate axes so that $\phi(\vec
r)=\phi(r^{\mu})$. A natural candidate for $\phi(r^{\mu})$ is $\cos(k_{\mu}r^{\mu})$ (no implied sum over repeated indices) with $k_{\mu}=2\pi n/L$, where $n=1,2,...$ In this case, $\rho_{\phi}$ is the $k^{th}$ mode of the cosine transform of the density. We will also consider the simpler function $\phi(r^{\mu})=|r^{\mu}|/L$. The absolute value corresponds to the case where all the particles feel a force along the $\mu$th direction pointing towards the origin. It gives results very similar to $\phi(r^{\mu})=\cos(k_{\mu}r^{\mu})$ for small $k$ at a fraction of the computational cost. (No sum over repeated indices.) So our results in this paper correspond to two cases: $$\rho_{\phi}=\sum_{i}|r^{\mu}_{i}|/L
\label{eq:abs}$$ which is rather like a center of mass, and $$\rho_{\phi}=\sum_{i}\cos(k_{\mu}r_{i}^{\mu})
