  The well known Bohr-van Leeuwen Theorem states that the orbital diamagnetism
of classical charged particles is identically zero in equilibrium. However,
results based on real space-time approach using the classical Langevin equation
predicts non-zero diamagnetism for classical unbounded (finite or infinite)
systems. Here we show that the recently discovered Fluctuation Theorems,
namely, the Jarzynski Equality or the Crooks Fluctuation Theorem surprisingly
predict a free energy that depends on magnetic field as well as on the friction
coefficient, in outright contradiction to the canonical equilibrium results.
However, in the cases where the Langevin approach is consistent with the
equilibrium results, the Fluctuation Theorems lead to results in conformity
with equilibrium statistical mechanics. The latter is demonstrated analytically
through a simple example that has been discussed recently.
