Realizing quasistatic processes in finite times requires additional control parameters to keep the system in instantaneous equilibrium (ieq). However, the finite-rate ieq transition of the reverse process is not just the time-reversal of the ieq forward process due to the odd-parity of controlling parameters. We theoretically show a work relation that the dissipated work of the ieq transition of the forward process is the same as that of the corresponding reverse process. The work relation can be interpreted as a generalization of equilibrium (quasistatic) processes. The work relation and the associated statistics of nonequilibrium work are experimentally confirmed in three different Brownian systems: the time-varying harmonic and non-harmonic potentials and the Brownian harmonic transport, which are manipulated by the optical feedback trap.

在有限时间内实现准静态过程需要附加的控制参数，以使系统保持瞬时平衡（ieq）。但是，由于控制参数的奇偶性，反向过程的有限速率ieq跃变不仅是ieq正向过程的时间反向。我们从理论上证明了一种工作关系，即正向过程的ieq过渡的耗散工作与相应的反向过程的耗散工作相同。功关系可以解释为平衡（准静态）过程的概括。在三个不同的布朗系统中通过实验证实了功关系和相关的非平衡功统计：时变谐波和非谐波电势以及布朗谐波传输，它们由光反馈陷阱控制。