论文标题
可逆系统和驱动系统的时间平均统计力学波动的光谱理论
Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems
论文作者
论文摘要
我们为一般非平衡初始条件提供了一种光谱理论方法，以实现时间平均水平的统计力学。我们考虑具有连续或离散状态空间的可逆性以及不可逆的千古随机动力学的有限的局部加性功能的统计数据。我们得出了从Fokker-Planck或Master方程动力学的基础发电机的特征性的时间平均观测值的平均值观察值的平均值，相关性的确切结果，并从物理角度讨论结果。 Feynman-kac公式是使用ItôCilculus重新衍生的，并结合了非热扰动理论。在频谱表示中，通用中心限制定律的出现在大偏差时间尺度上明确显示。对于具有平衡的初始条件的可逆动力学，我们根据回报概率的积分来得出一般的上限与职业措施的波动。分析简单的，准确的可解决的示例，以说明如何应用理论。作为一个生物物理的例子，我们对单个受体的浓度测量的精确度重新审视了伯格细胞问题。我们的结果直接适用于以物理，化学，生物学和经济系统中的时间平均值可观察力和添加剂功能为基础的各种现象。
We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic stochastic dynamics with continuous or discrete state-space. We derive exact results for the mean, fluctuations and correlations of time average observables from the eigenspectrum of the underlying generator of Fokker-Planck or master equation dynamics, and discuss the results from a physical perspective. Feynman-Kac formulas are re-derived using Itô calculus and combined with non-Hermitian perturbation theory. The emergence of the universal central limit law in a spectral representation is shown explicitly on large deviation time-scales. For reversible dynamics with equilibrated initial conditions we derive a general upper bound to fluctuations of occupation measures in terms of an integral of the return probability. Simple, exactly solvable examples are analyzed to demonstrate how to apply the theory. As a biophysical example we revisit the Berg-Purcell problem on the precision of concentration measurements by a single receptor. Our results are directly applicable to a diverse range of phenomena underpinned by time-average observables and additive functionals in physical, chemical, biological, and economical systems.
