We consider the application of the fluctuation dissipation theorem to the electrodynamics of Aharonov-Bohm, which differs from Maxwell's electrodynamics in that it allows for local nonconservation of charge. For the case of a system of nonconserved 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 the Maxwell case, while the magnetic contribution is the same as in Maxwell theory; the electric excess energy is compensated by a negative contribution arising from the Aharonov-Bohm scalar field. For a conductor with local nonconservation 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.

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• Fluctuation-dissipation theorem