  The isothermal compressibility of an interacting or non interacting system
may be extracted from the fluctuations of the number of particles in a well
chosen control volume. Finite size effects are prevalent and should then be
accounted for to obtain a meaningful, thermodynamic compressibility. In the
traditional computational setup where a given simulation box is replicated with
periodic boundary conditions, we study particle number fluctuations outside the
box (i.e. when the control volume exceeds the box itself), which bear relevant
thermodynamic information. We also investigate the related problem of
extracting the compressibility from the structure factor in the small
wave-vector limit ($k\to 0$). The calculation should be restricted to the
discrete set of wave-vectors $k$ that are compatible with the periodicity of
the system, and we assess the consequences of considering other $k$ values, a
widespread error among beginners.
