  The quantum ergotropy quantifies the maximal amount of work that can be
extracted from a quantum state without changing its entropy. Given that the
ergotropy can be expressed as the difference of quantum and classical relative
entropies of the quantum state with respect to the thermal state, we define the
classical ergotropy, which quantifies how much work can be extracted from
distributions that are inhomogeneous on the energy surfaces. A unified approach
to treat both quantum as well as classical scenarios is provided by geometric
quantum mechanics, for which we define the geometric relative entropy. The
analysis is concluded with an application of the conceptual insight to
conditional thermal states, and the correspondingly tightened maximum work
theorem.
