  The recently developed exact factorization approach condenses all electronic
effects on the nuclear subsystem into scalar and vector potentials that appear
in an effective time dependent Schr\"{o}dinger equation. Starting from this
equation, we derive subsystem Ehrenfest identities characterizing the energy,
momentum and angular momentum transfer between electrons and nuclei. An
effective electromagnetic force operator induced by the electromagnetic field
corresponding to the effective scalar and vector potentials appears in all
three identities. The effective magnetic field has two components that can be
identified with the Berry curvature calculated with (a) different cartesian
coordinates of the same nucleus and (b) arbitrary cartesian coordinates of two
different nuclei. (a) has a classical interpretation as the induced magnetic
field felt by the nucleus, while (b) has no classical analog. Subsystem
Ehrenfest identities are ideally suited for quantifying energy transfer in
electron-phonon systems. With two explicit examples we demonstrate the
usefulness of the new identities.
