  We derive a generalization of the Ehrenfest theorem valid for open quantum
systems. From this result, we identify three factors contributing to the
evolution of expected values: explicit time dependence of the observable,
thermal interaction, and quantum coherence. When considering the local
Hamiltonian as the observable, we obtain an alternative version of the first
law of thermodynamics. In some cases, the non-thermal contributions to the
energy rate of change can be expressed as the expected value of a Hermitian
operator, so the power performed by the system can be considered a quantum
observable. As an application, the pure dephasing process is reinterpreted from
this perspective.
