Pietzonka Patrick, Ritort Felix, Seifert Udo
II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany.
Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain.
Phys Rev E. 2017 Jul;96(1-1):012101. doi: 10.1103/PhysRevE.96.012101. Epub 2017 Jul 5.
For fluctuating currents in nonequilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales. This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite time scales are not accessible. Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit. We illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle.
对于非平衡稳态下的波动电流，最近发现的热力学不确定性关系表达了它们的方差与驱动相关的整体熵成本之间的基本关系。我们表明，这种关系不仅适用于由大偏差理论描述的波动的长时间极限，也适用于任意有限时间尺度上的波动。这种推广便于将热力学不确定性关系应用于单分子实验，因为在单分子实验中无法达到无限时间尺度。重要的是，通常这种关系的有限时间变体允许推断出一个比从长时间极限获得的熵产生界限更强的界限。我们通过随机切换的激光镊子对捕获的胶体粒子所做的波动功来说明这种关系。
