Fluctuations in Aharonov-Bohm Electrodynamics

We consider the application of the Fluctuation Dissipation Theorem (FDT) to the electrodynamics of Aharonov-Bohm (ABE), which differs from Maxwell's in that it allows for local non-conservation of charge. For the case of a system of non-conserved charges at thermal equilibrium we obtain the same spectral distribution of energy of the electromagnetic field as in Maxwell electrodynamics. However, the electric field contribution to that energy doubles that in Maxwell case, while the magnetic contribution is the same as in Maxwell theory, the electric excess energy is compensated by a negative contribution arising form the Aharonov-Bohm (AB) scalar field. For a conductor with local non-conservation of charge described by the $\gamma$ model, we derive the spectrum of current correlation at first order in $\gamma$, which results in a violet noise contribution added to the classical Johnson-Nyquist white noise result for the voltage fluctuations in a conductor.