# Periodic boundary conditions

A liquid, in the thermodynamic limit, would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones computer simulation. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as **periodic boundary conditions**. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods ^{[1]}, where one can imagine the action takes place on the surface of a torus.
In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a phase transition, where long-range fluctuations play an important role, problems may arise.

## References

**Related reading**

- M. J. Mandell "On the properties of a periodic fluid", Journal of Statistical Physics
**15**pp. 299-305 (1976) - Lawrence R. Pratt and Steven W. Haan "Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory", Journal of Chemical Physics
**74**pp. 1864- (1981)

## External resources

- Periodic boundary conditions in various geometries sample FORTRAN computer code from the book M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989).