  We derive expressions for the expectation values of the local energy and the
local power transferred by an external electrical field to a many-particle
system of interacting spinless electrons. In analogy with the definition of the
(local) presence and current probability densities, we construct a local energy
operator such that the time-rate of change of its expectation value provides
information on the spatial distribution of power. Results are presented as
functions of an arbitrarily small volume $\Omega$, and physical insights are
discussed by means of the quantum hydrodynamical representation of the
wavefunction, which is proven to allow for a clear-cut separation into
contributions with and without classical correspondence. Quantum features of
the local power are mainly manifested through the presence of non-local
sources/sinks of power and through the action of forces with no classical
counterpart. Many-particle classical-like effects arise in the form of
current-force correlations and through the inflow/outflow of energy across the
boundaries of the volume $\Omega$. Interestingly, such intriguing features are
only reflected in the expression for the local power when the volume $\Omega$
is finite. Otherwise, for closed systems with $\Omega \to \infty$, we recover a
classical-like single-particle expression.
