  In this study the power flow in a coupled mechanical and electromagnetic
harvesting system in presence of both positional and electrical fluctuations is
analyzed. Explicit expressions for the power into and out of the mechanical and
electrical parts of the system are found in the case of weak coupling, and it
is shown how the power flows between the domains consistent with energy
conservation. The case of thermal fluctuations is considered in particular, and
use of the fluctuation-dissipation theorem explicitly demonstrates that the
power delivered to the mechanical system from the electrical system is the same
as the power delivered to the electrical system from the mechanical system. On
the other hand, the power dissipated in the electrical circuit is not the same
as the power transferred from the mechanical domain if the electrical circuit
contains its own current fluctuations. The electrical noise power dissipated in
a load resistor is calculated, and found to consist of a component due to
electromagnetic coupling in addition to the well-known Nyquist component. The
component due to electromagnetic coupling scales with size, and becomes more
important than the Nyquist component only for sufficiently small systems.
