标题： 基于不完全观测的可部分访问马尔可夫网络的熵估计：有限分辨率和有限统计的作用 显示英文标题

标题： Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics

摘要： 从实际观测数据中估计熵产生可能很困难，这是由于空间和时间上的有限分辨率以及有限的测量统计量。 我们表征了由有限样本大小引入的统计误差，并在这些限制下比较了三种不同的熵估计器在两种不同的典型系统中的性能，一个四状态马尔可夫网络和一个改进的米氏-门尼反应模型。 我们考虑了热力学不确定性关系，一种基于等待时间的解析跃迁估计器和一种在不完美观测场景下的基于等待时间的模糊跃迁估计器。 对于完美的测量统计量和有限的时间分辨率，基于解析跃迁的估计器在所有考虑的场景中表现最佳。 在低驱动亲和力下，热力学不确定性关系给出的估计优于基于模糊跃迁的估计器，而在高驱动亲和力下，后者表现更好。 此外，我们发现更高的时间和空间分辨率会导致测量统计量的收敛变慢，这意味着在短测量时间内，较低的分辨率可能是有益的。 此外，我们发现基于等待时间的熵估计器存在一种自平均效应，这可以减少有限统计观测的方差。 显示英文摘要

摘要： Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare the performance of three different entropy estimators under these limitations for two different paradigmatic systems, a four-state Markov network and an augmented Michaelis-Menten reaction scheme. We consider the thermodynamic uncertainty relation, a waiting-time based estimator for resolved transitions and a waiting-time based estimator for blurred transitions in imperfect observation scenarios. For perfect measurement statistics and finite temporal resolution, the estimator based on resolved transitions performs best in all considered scenarios. The thermodynamic uncertainty relation gives a better estimate than the estimator based on blurred transitions at low driving affinities, whereas the latter performs better at high driving affinities. Furthermore, we find that a higher temporal and spatial resolution leads to slower convergence of measurement statistics, implying that for short measurement times, a lower resolution may be beneficial. Additionally, we identify a self-averaging effect for the waiting-time based entropy estimators that can reduce their variance for observations with finite statistics.