Is Polarization Inconsistent with Classical Electricity? I had read that the Bohr-Van Leeuwen theorem shows paramagnetism to be impossible with only classical magnetism. It has been explained to me that magnetism is ultimately a quantum effect. Is there an analogous result with electricity?
The motivation for this question comes from the idea that in certain situations and from a certain frame of reference you can "turn" a purely magnetic effect into a purely electrical effect. If this is true, then would the results of the Bohr-Van Leeuwen theorem apply to electricity as well by default?
 A: The Bohr-van Leeuwen theorem states that a system of charged particles that obeys Boltzmann's probability distribution won't get magnetized by external magnetic field, diamagnetically or paramagnetically.
The Boltzmann distribution of momenta of charged particles does not allow for preferred direction of electric currents on the surface of the body(or magnetic domain), because boltzmannian distribution of momenta in thermal equilibrium is isotropic, even in external magnetic field.
In a classical model of magnetism (Ampere's model), magnetized state of macroscopic bodies is due to molecular currents, which have non-zero density on the surface of the body(magnetic domain). The Boltzmann distribution is inconsistent with this model.
In other words, the Bohr-van Leeuwen result is because the boltzmannian assumption prevents the presence of macroscopic electric current, which is necessary for magnetized state.
For macroscopic electrically polarized state, no electric current is necessary, and the use of the Boltzmann distribution does not prevent external electric field from polarizing the body. So the theorem is not relevant for electric polarization in external electric field.

the idea that in certain situations and from a certain frame of reference you can "turn" a purely magnetic effect into a purely electrical effect.

This is not the case here. In discussion of electric polarization effects of external electric field on material body, there is a preferred frame - the frame of the body.
