Jarzynski Equality for Conditional Stochastic Work

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.

Automated summary

In this study, a novel notion of conditional stochastic work for classical, Hamiltonian dynamics is proposed, inspired by the one-time measurement approach, which is built upon the change of expectation value of energy conditioned on the initial energy surface. The main results include a generalized Jarzynski equality and a sharper maximum work theorem, accounting for the non-adiabaticity of the process, and are illustrated with the parametric harmonic oscillator.