论文标题
一维棕色粒子具有随机重置为随机位置的第一通道时间和信息
First passage time and information of a one-dimensional Brownian particle with stochastic resetting to random positions
论文作者
论文摘要
我们探讨了随机重置到布朗粒子的随机位置对第一次通道时间和香农熵的影响。我们探索了不同的熵制度，即\ textit {外部驱动}，\ textit {Zero-entropy}和\ textit {maxwell demon}制度。我们表明，在任何这些制度中，都可以找到平均第一个通过时间（MPFT）。我们提供了一种新颖的分析方法来计算MFPT，平均第一次通过的重置数（MFPNR）和平均第一个传递熵（MFPE），如果布朗粒子重置为从一组分布中采样的随机位置\ textit \ textit {a先验{a a先验}。我们显示了重置位置分布的第二刻与复位率之间的相互作用，以及它对MFPT和MFPE的影响。我们进一步提出了一种机制，每次重置的熵可以在麦克斯韦恶魔或外部驱动的方案中，但总体平均第一句经通道熵对应于零透镜制度。此外，我们发现动态相空间与熵相空间之间的重叠。我们通过假设重置位置是随机的并从高斯分布中采样的，我们在Evans-Majumdar模型的广义版本中使用此方法。然后，我们考虑\ textIt {切换reset}，从而将布朗粒子重置为从分布的随机位置，取决于复位奇偶校验。我们的所有结果均与数值模拟并一致并一致。
We explore the effects of stochastic resetting to random positions of a Brownian particle on first passage times and Shannon's entropy. We explore the different entropy regimes, namely, the \textit{externally-driven}, the \textit{zero-entropy} and the \textit{Maxwell demon} regimes. We show that the mean first passage time (MPFT) minimum can be found in any of these regimes. We provide a novel analytical method to compute the MFPT, the mean first passage number of resets (MFPNR) and mean first passage entropy (MFPE) in the case where the Brownian particle resets to random positions sampled from a set of distributions known \textit{a priori}. We show the interplay between the reset position distribution's second moment and the reset rate, and the effect it has on the MFPT and MFPE. We further propose a mechanism whereby the entropy per reset can be either in the Maxwell demon or the externally driven regime, yet the overall mean first passage entropy corresponds to the zero-entropy regime. Additionally, we find an overlap between the dynamic phase space and the entropy phase space. We use this method in a generalized version of the Evans-Majumdar model by assuming the reset position is random and sampled from a Gaussian distribution. We then consider the \textit{toggling reset} whereby the Brownian particle resets to a random position sampled from a distribution dependent on the reset parity. All our results are compared to and in agreement with numerical simulations.
