  It has been established that the inclusive work for classical, Hamiltonian
dynamics is equivalent to the two-time energy measurement paradigm in isolated
quantum systems. However, a plethora of other notions of quantum work has
emerged, and thus the natural question arises whether any other quantum notion
can provide motivation for purely classical considerations. In the present
analysis, we propose the conditional stochastic work for classical, Hamiltonian
dynamics, which is inspired by the one-time measurement approach. This novel
notion is built upon the change of expectation value of the energy conditioned
on the initial energy surface. As main results we obtain a generalized
Jarzynski equality and a sharper maximum work theorem, which account for how
non-adiabatic the process is. Our findings are illustrated with the parametric
harmonic oscillator.
