Jarzynski equality for conditional stochastic work

TL;DR

This paper introduces a new concept of conditional stochastic work for classical Hamiltonian systems, deriving a generalized Jarzynski equality and maximum work theorem that account for non-adiabatic effects, with applications to harmonic oscillators.

Contribution

It proposes the conditional stochastic work notion inspired by one-time measurement, extending classical and quantum work relations and providing sharper bounds for work in non-adiabatic processes.

Findings

Derived a generalized Jarzynski equality for conditional stochastic work.

Established a sharper maximum work theorem considering non-adiabaticity.

Illustrated results with the parametric harmonic oscillator.

Abstract

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.