AI 中文总结
该研究将多维热力学不确定性关系推广至含任意初始态、任意时长的随时间驱动过程，覆盖多类计数可观测量与粗粒化观测，统一相关估计方法并通过示例阐释。
AI 中文摘要
不确定性关系为部分可访问马尔可夫网络的隐藏量提供下界，例如平均熵产生率和总动力学活性，其中热力学不确定性关系（TUR）是最具代表性的，涉及涨落净电流的精度。其主要推广形式之一是多维热力学不确定性关系（MTUR），通过使用一组观测净电流的协方差得到更紧的界。我们将该界推广至具有任意初始态和任意测量时长的随时间驱动的过程，该界可用于一组涨落计数可观测量，每个可观测量可为时间反对称、时间对称或时间非对称，即净电流、流量或流。我们甚至允许粗粒化观测，其中每个计数可观测量可包含底层系统的多个不可区分观测跃迁。由此，我们统一推广了MTUR、基于单个电流的随时间过程TUR扩展、以及基于单个通量或单个流量的估计器，并用简单示例阐释了该通用不确定性关系。
英文摘要
Uncertainty relations provide lower bounds for otherwise hidden quantities of a partially accessible Markov network like the mean entropy production rate and the total dynamical activity. The thermodynamic uncertainty relation (TUR) is arguably the most prominent one and involves the precision of a fluctuating net current. One of its major generalizations is the multidimensional TUR (MTUR), which yields a tighter bound by using covariances of a set of observed net currents. We generalize this latter bound to time-dependently driven processes with arbitrary initial state and arbitrary measurement duration. Furthermore, this bound can be used with a set of fluctuating counting observables each of which can be time-antisymmetric, time-symmetric or time-asymmetric, i.e., a net current, a traffic or a flow. We can even allow for coarse-grained observations in which each counting observable could consist of multiple indiscernable observed transitions of the underlying system. Thus, we generalize the MTUR, extensions of the TUR for time-dependent processes based on one current, and an estimator based on one flux or on one traffic in a unifying way. We illustrate this general uncertainty relation with simple examples.
