Quantum force due to distinct boundary conditions

We calculate the quantum statistical force acting on a partition wall that divides a one dimensional box into two halves. The two half boxes contain the same (fixed) number of noninteracting bosons, are kept at the same temperature, and admit the same boundary conditions at the outer walls; the only difference is the distinct boundary conditions imposed at the two sides of the partition wall. The net force acting on the partition wall is nonzero at zero temperature and remains almost constant for low temperatures. As the temperature increases, the force starts to decrease considerably, but after reaching a minimum it starts to increase, and tends to infinity with a square-root-of-temperature asympotics. This example demonstrates clearly that distinct boundary conditions cause remarkable physical effects for quantum systems.