Iyori Tasuku, Izumida Yuki
Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan.
Phys Rev E. 2024 Jan;109(1-1):014138. doi: 10.1103/PhysRevE.109.014138.
The thermodynamic uncertainty relation (TUR) is an inequality showing the tradeoff relationship between the relative fluctuation of current observables and thermodynamic costs. It is one of the most important results of stochastic thermodynamics. There are various applications for TUR, one of which is the recent finding of thermodynamic constraints on the time window in which anomalous diffusion of Brownian particles can occur, including subdiffusion and superdiffusion, which are slower and faster than normal diffusion, respectively. These constraints are quite nontrivial because they are not generally derived from the asymptotic normal-diffusive behavior of the anomalous diffusion itself. In this study, we applied multidimensional TUR to the subdiffusion of Brownian particles obeying multivariate Langevin dynamics with a translationally invariant Hamiltonian in equilibrium. Multidimensional TUR is an improved TUR that includes information on another observable in addition to the one currently being considered. The use of an additional observable yields tighter bounds on the current fluctuation than those obtained using TUR. As an example, we demonstrated our theory using the one-dimensional Rouse model, which is known as a simple and analytically tractable model of polymer chains. We demonstrated that we improved the bounds for the persistence time of subdiffusion of the Rouse model, which became tighter as a more correlated observable with the current was used.
热力学不确定性关系（TUR）是一个不等式，它展示了当前可观测量的相对涨落与热力学成本之间的权衡关系。它是随机热力学最重要的成果之一。TUR有多种应用，其中之一是最近发现了对布朗粒子反常扩散（包括分别比正常扩散慢和快的亚扩散和超扩散）可能发生的时间窗口的热力学约束。这些约束相当不平凡，因为它们通常不是从反常扩散本身的渐近正态扩散行为推导出来的。在本研究中，我们将多维TUR应用于服从具有平移不变哈密顿量的多元朗之万动力学的布朗粒子的亚扩散，该系统处于平衡态。多维TUR是一种改进的TUR，除了当前正在考虑的可观测量外，还包括关于另一个可观测量的信息。使用额外的可观测量会比使用TUR得到的当前涨落界限更严格。作为一个例子，我们用一维劳斯模型展示了我们的理论，该模型是聚合物链的一个简单且易于解析处理的模型。我们证明了我们改进了劳斯模型亚扩散持续时间的界限，随着使用与当前更相关的可观测量，这些界限变得更严格。
