Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen.
Phys Rev Lett. 2023 Feb 24;130(8):087101. doi: 10.1103/PhysRevLett.130.087101.
Thermodynamic uncertainty relations (TURs) bound the dissipation in nonequilibrium systems from below by fluctuations of an observed current. Contrasting the elaborate techniques employed in existing proofs, we here prove TURs directly from the Langevin equation. This establishes the TUR as an inherent property of overdamped stochastic equations of motion. In addition, we extend the transient TUR to currents and densities with explicit time dependence. By including current-density correlations we, moreover, derive a new sharpened TUR for transient dynamics. Our arguably simplest and most direct proof, together with the new generalizations, allows us to systematically determine conditions under which the different TURs saturate and thus allows for a more accurate thermodynamic inference. Finally, we outline the direct proof also for Markov jump dynamics.
热力学不确定性关系 (TURs) 通过观测电流的涨落从下限定义非平衡系统的耗散。与现有证明中使用的精巧技术形成对比，我们在此直接从朗之万方程证明 TURs。这将 TUR 确立为过阻尼随机运动方程的固有特性。此外，我们还将瞬态 TUR 扩展到具有显式时间依赖性的电流和密度。通过包含电流-密度相关，我们进一步推导出瞬态动力学的新的更精确的 TUR。我们的证明可以说是最简单和最直接的，并且具有新的概括，这使我们能够系统地确定不同 TUR 饱和的条件，从而可以进行更准确的热力学推断。最后，我们还概述了 Markov 跳跃动力学的直接证明。
