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

TL;DR

This paper demonstrates that classical diamagnetism does not exist for charged particles on curved surfaces and confirms the validity of fluctuation theorems in such geometries, challenging recent claims of nonzero diamagnetic moments.

Contribution

It proves that classical Langevin dynamics on curved surfaces leads to zero magnetic moment and validates fluctuation theorems in this setting, countering previous numerical claims.

Findings

Classical Langevin dynamics yields zero average magnetic moment on curved surfaces.

The Bohr-van Leeuwen theorem applies to particles on curved geometries.

Nonequilibrium fluctuation theorems hold for many-particle systems on curved surfaces.

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.