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.

已经确定，经典的哈密顿动力学的包容性工作等同于孤立量子系统中的两次能量测量范式。但是，出现了许多其他的量子功概念，因此自然而然地产生了一个问题，即是否有任何其他的量子概念可以为纯粹的经典考虑提供动力。在目前的分析中，我们提出了条件随机工作对于经典的汉密尔顿动力学，它受到一次性测量方法的启发。这个新颖的概念是建立在初始能量表面上的能量期望值变化的基础上的。作为主要结果，我们获得了广义的Jarzynski等式和更清晰的最大功定理，这说明了该过程的绝热程度。参数谐波振荡器说明了我们的发现。