The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of observable functions-referred to as functional-diffusion. This is not the same as the system's individual trajectories, but can be regarded as a meta-trajectory. Following this idea, we measure how the approach to ergodicity evolves over time for the observed magnetization of a full Ising model with an external field. We compute the diffusive behavior of the functional across a range of temperatures via Metropolis and Glauber single-spin-flip dynamics. The system's ensemble-averaged dynamics are computed using expressions from the exact solution. Power-law behavior in the approach to ergodicity provides a classification of anomalies in functional-diffusion, demonstrating nonlinear anomalous behavior over different temperature and field ranges. Studying the ergodicity convergence of these meta-trajectories can help validate and enhance the pedagogical understanding of nonequilibrium thermodynamic systems.
Tuning ergodicity breaking: Anomalous diffusion under asymptotic power-law forcing
Instituto Latino-Americano de Ciências da Vida e da Natureza, Universidade Federal da Integração Latino-Americana（拉丁美洲生命与自然科学研究所，拉丁美洲联邦大学）；Instituto de Ciencias, Universidad Nacional de General Sarmiento（科学与综合学院，圣马丁国立大学）；National Scientific and Technical Research Council（国家科学技术研究委员会）
Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
Tokyo University of Science（东京科学大学）；Pohang University of Science and Technology（浦项科技大学）；Asia Pacific Centre for Theoretical Physics（亚太理论物理中心）；University of Potsdam（波茨坦大学）；Wakayama University（和歌山大学）；Nagoya University（名古屋大学）；Keio University（庆应义塾大学）
Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation
研究了在周期势场中运动的惯性布朗粒子的远平衡输运。如最近对于SQUID棘轮动力学（Spiechowicz J. & Luczka J. Phys. Rev. E 91，062104（2015））所检测到的，粒子位置与其平均值的均方差可能涉及三个不同的中间扩散机制，尽管是扩展的扩散机制：最初是超扩散，然后是亚扩散，最后是渐近长时间限制中的正常扩散。尽管这些异常是瞬态效应，但它们的寿命可能比设置的特征时间尺度长很多很多个数量级，并且对温度或潜在不对称性等系统参数非常敏感。在本文中，我们揭示了与系统的遍历性，对称性破缺的周期势和超低松弛的粒子速度向其稳定状态的扩散异常的机制。类似的扩散行为序列可以在各种系统中检测到，包括，除其他外，在随机电位的胶体颗粒，玻璃形成液体和粒状气体。
Genuine and spurious (non-)ergodicity in single particle tracking
University of Potsdam（波茨坦大学）；LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所）；Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；Institut für Physik, Humboldt-Universität zu Berlin（柏林洪堡大学物理研究所）；Asia Pacific Centre for Theoretical Physics（亚太理论物理中心）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微观结构物理研究所）；Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology（弗罗茨瓦夫科技大学纯与应用数学学院）；Akhiezer Institute for Theoretical Physics, National Science Center, Kharkiv Institute of Physics and Technology（哈尔科夫物理与技术国家科学中心阿赫谢泽理论物理研究所）
最近的一篇论文[M。H. Lee，Phys. Rev. Lett. 98，190601（2007）]已经引起了人们的注意，不可逆性是一个比遍历性更广泛的概念，因此Khinchin定理[A. I. Khinchin，Mathematical Foundations of统计力学（Dover，New York）1949]可能在某些系统中失败。在这封信中，我们表明，对于广义朗之万方程所描述的正常和异常扩散的所有范围，欣钦定理成立。
