Nonexistence of classical diamagnetism and nonequilibrium fluctuation theorems for charged particles on a curved surface

Abstract

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.

6 pages; typos corrected

References in corpus (3)

• Fluctuation theorems for stochastic dynamics
• Nonequilibrium Work distributions for a trapped Brownian particle in a time dependent magnetic field
• Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

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