A single particle is contained in a vessel of volume 2V which is divided into two equal sub-volumes by a partition with a small hole in it. The particle carries an electric charge, and the hole in the partition is the site of a localized electric field; the net effect is that the particle has a potential energy of zero on one side of the partition, and of εe on the other side. What is the probability that the particle will be found in the zero-potential half of the vessel, if the system is maintained in equilibrium at temperature T? How would this result be affected by internal modes of the particles? How would the result be affected if the dispersion relation of the particles were such that the energy was proportional to the momentum, rather than to its square? If the container were to contain one mole of an ideal gas (non-interacting particles despite the electric charge on each!) what would be the pressure in each sub-volume?