Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden.
Phys Rev E. 2019 Nov;100(5-1):052137. doi: 10.1103/PhysRevE.100.052137.
Thermodynamic uncertainty relations quantify how the signal-to-noise ratio of a given observable is constrained by dissipation. Fluctuation relations generalize the second law of thermodynamics to stochastic processes. We show that any fluctuation relation directly implies a thermodynamic uncertainty relation, considerably increasing their range of applicability. In particular, we extend thermodynamic uncertainty relations to scenarios which include measurement and feedback. Since feedback generally breaks time-reversal invariance, the uncertainty relations involve quantities averaged over the forward and the backward experiment defined by the associated fluctuation relation. This implies that the signal-to-noise ratio of a given experiment can in principle become arbitrarily large as long as the corresponding backward experiment compensates, e.g., by being sufficiently noisy. We illustrate our results with the Szilard engine as well as work extraction by free energy reduction in a quantum dot.
热力学不确定性关系量化了给定可观测量的信噪比如何受到耗散的限制。涨落关系将热力学第二定律推广到随机过程。我们表明，任何涨落关系都直接暗示了热力学不确定性关系，大大增加了它们的适用范围。特别是，我们将热力学不确定性关系扩展到包括测量和反馈的情况。由于反馈通常会破坏时间反演不变性，因此不确定性关系涉及到由相关涨落关系定义的正向和反向实验中平均的量。这意味着，只要对应的反向实验进行补偿，例如通过足够的噪声，给定实验的信噪比原则上可以任意增大。我们用 Szilard 引擎以及在量子点中通过自由能减少来提取功来说明我们的结果。
