On the Bohr-van Leeuwen theorem, the non-existence of classical magnetism in thermal equilibrium

We point out that the classical Langevin equation for a charged particle moving on a ring in a constant magnetic field perpendicular to the ring leads at long times to thermal equilibrium and to zero magnetic moment, consistent with the Bohr-van Leeuwen theorem. This fact is a counter-example to the recent claim that the Langevin equation leads to a non-zero diamagnetic moment in thermal equilibrium when the particle moves in a finite but unbounded space.