  We show that the classical Langevin dynamics for a charged particle on a
closed curved surface in a time-independent magnetic field leads to the
canonical distribution in the long time limit. Thus the Bohr-van Leeuwen
theorem holds even for a finite system without any boundary and the average
magnetic moment is zero. This is contrary to the recent claim by Kumar and
Kumar (EPL, {\bf 86} (2009) 17001), obtained from numerical analysis of
Langevin dynamics, that a classical charged particle on the surface of a sphere
in the presence of a magnetic field has a nonzero average diamagnetic moment.
We extend our analysis to a many-particle system on a curved surface and show
that the nonequilibrium fluctuation theorems also hold in this geometry.

Statistical Mechanics