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We derive expressions for the expectation values of the local energy and thelocal power transferred by an external electrical field to a many-particlesystem of interacting spinless electrons. In analogy with the definition of the(local) presence and current probability densities, we construct a local energyoperator such that the time-rate of change of its expectation value providesinformation on the spatial distribution of power. Results are presented asfunctions of an arbitrarily small volume $\Omega$, and physical insights arediscussed by means of the quantum hydrodynamical representation of thewavefunction, which is proven to allow for a clear-cut separation intocontributions with and without classical correspondence. Quantum features ofthe local power are mainly manifested through the presence of non-localsources/sinks of power and through the action of forces with no classicalcounterpart. Many-particle classical-like effects arise in the form ofcurrent-force correlations and through the inflow/outflow of energy across theboundaries of the volume $\Omega$. Interestingly, such intriguing features areonly reflected in the expression for the local power when the volume $\Omega$is finite. Otherwise, for closed systems with $\Omega \to \infty$, we recover aclassical-like single-particle expression.

Local energy and power for many-particle quantum systems driven by an external electrical field