Charged particle in a magnetic field: Jarzynski equality.

We describe some solvable models which illustrate the Jarzynski theorem and related fluctuation theorems. We consider a charged particle in the presence of a magnetic field in a two-dimensional harmonic well. In the first case the center of the harmonic potential is translated with a uniform velocity, while in the other case the particle is subjected to an ac force. We show that the Jarzynski identity complements the Bohr-van Leeuwen theorem on the absence of diamagnetism in an equilibrium classical system.