I am having a lot of trouble understanding the influence of volume on relative permittivity/static dielectric constant. I'm not a chemist, but am using molecular dynamics to calculate relative permittivity for use in other work.
A predecessor used this equation for relative permittivity $ε_\mathrm{r}$:
$$ε_\mathrm{r} = 1 + \frac{4π\sigma_M}{3k_\mathrm{B}TV}$$
where $V$ is the volume of the simulation, $T$ is temperature, $\sigma_M$ is the variance of the total dipole moment, and $k_\mathrm{B}$ is the Boltzmann constant.
Here is what I do not understand: If I use a different $V $(i.e., a different number of atoms) for my simulation compared to my predecessor, then my calculated relative permittivity will be different from his. I have done this to make sure, and indeed, the difference is quite significant.
Is there something silly I am misunderstanding here? Like "$V$" is not the average box/cell volume of the simulation, but something that is not size-dependent?