AI 中文总结
该研究针对时间依赖驱动的开放量子系统，推导出功的热力学不确定性关系，结合量子费希尔信息给出两个热力学界限，并在二能级系统中验证其依赖于驱动协议和切换时间尺度。
AI 中文摘要
我们推导了一个热力学不确定性关系，适用于由时间依赖协议驱动并经历重复投影能量测量的开放量子系统。该协议由一系列协议淬火表示，淬火之间由有限时间的林德布拉德演化分隔，因此功在淬火时累积，而耗散发生在淬火之间。由此产生的功统计满足加洛韦-科恩对称性，从而得出克鲁克斯和雅尔津斯基涨落关系。通过扰动耗散动力学并将克拉默-拉奥不等式与量子费希尔信息相结合，我们得到 $\mathrm{Var}\\,{\cal W}/[τ\partial_τ\langle{\cal W}\rangle]^2\ge 1/{\cal F}\ge\max(1/{\cal A},2/{\cal E})$，其中 $\langle{\cal W}\rangle$ 是功的期望值，$\mathrm{Var}\\,{\cal W}$ 是功的方差，${\cal F}$ 是费希尔信息，${\cal A}$ 是动力学活性，${\cal E}$ 是无量纲熵产生，$τ$ 是淬火之间的切换时间间隔。这两个热力学界限源自两个独立的扰动，它们产生功统计的相同响应。我们以方波和正弦驱动下的耗散二能级系统为例说明了该关系，并表明更严格的热力学界限可能取决于驱动协议和切换时间尺度。
英文摘要
We derive a thermodynamic uncertainty relation for work in an open quantum system driven by a time-dependent protocol and subject to repeated projective energy measurements. The protocol is represented by a sequence of protocol quenches separated by finite-time Lindblad evolution, so that work is accumulated at the quenches while dissipation occurs between them. The resulting work statistics obey the Gallavotti-Cohen symmetry to give rise to the Crooks and Jarzynski fluctuation relations. By perturbing the dissipative dynamics and combining the Cramér--Rao inequality with the quantum Fisher information, we obtain $\mathrm{Var}\,W/[τ\partial_τ\langle W\rangle]^2\ge 1/F\ge\max(1/A,2/E)$, where $\langle W\rangle$ is the work expectation value, $\mathrm{Var}\,W$ is the variance of work, $F$ is the Fisher information, $A$ is the dynamical activity, $E$ is the dimensionless entropy production, and $τ$ is the switching time interval between quenches. The two thermodynamic bounds follow from two independent perturbations that generate the same response of the work statistics. We illustrate the relation for a dissipative two-level system under square-wave and sinusoidal driving and show that the tighter thermodynamic bound can depend on the driving protocol and switching time scale.
Comments5 pages, 3 figures, 1 supplementary material
