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.