论文标题
在连续空间稳态中粗砂的经验密度和电流
Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States
论文作者
论文摘要
我们介绍了描述和理解所有时间尺度上经验密度和稳态扩散过程的相关性和波动所需的概念和技术背景 - 可观察到统计力学和单个轨迹水平的热力学的核心。我们专注于空间粗粒的重要和非平凡效应。利用广义的时间反转对称性，我们提供了有关粗粒粒度经验密度和电流波动的物理含义的更深入的见解，并解释了为什么粗粒度量表的系统变化为推断系统耗散的界限提供了有效的方法。此外，我们讨论了经验密度和当前的统计数据以及中央限制机构中的统计数据。从更广泛的角度来看，我们的工作促进了随机演算作为Feynman-KAC理论和路径综合方法的强大直接替代方案的应用。
We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to statistical mechanics and thermodynamics on the level of individual trajectories. We focus on the important and non-trivial effect of a spatial coarse graining. Making use of a generalized time-reversal symmetry we provide deeper insight about the physical meaning of fluctuations of the coarse-grained empirical density and current, and explain why a systematic variation of the coarse-graining scale offers an efficient method to infer bounds on a system's dissipation. Moreover, we discuss emerging symmetries in the statistics of the empirical density and current, and the statistics in the central-limit regime. More broadly our work promotes the application of stochastic calculus as a powerful direct alternative to Feynman-Kac theory and path-integral methods.
