AI 中文总结
该研究扩展宏观涨落理论框架，求解非平稳扩散系统的多时间统计，揭示初始条件对电流涨落与分数布朗运动关联的影响，并通过微观动力学和数值模拟验证结果。
AI 中文摘要
电流涨落的统计长期以来是非平衡物理学的核心研究对象，现有多数研究聚焦于单次统计，而其多时间推广的探索相对较少。我们通过扩展宏观涨落理论（Macroscopic Fluctuation Theory, MFT）的涨落流体动力学框架，研究无限直线上扩散系统非平稳态的多时间统计，以填补这一空白。针对无相互作用格气和硬核布朗点粒子这类最简单情形，我们给出MFT的显式解，得到多时间大偏差统计；对于一般系统，通过微扰法求解MFT，得到两次时间关联的显式结果，这些结果表明，此前在平坦初始条件下观测到的电流涨落与分数布朗运动的关联，在阶跃初始条件下不再成立。我们通过求解无相互作用气体和对称简单排斥过程对应的微观动力学，独立验证了这些流体动力学结果，数值模拟也进一步提供了验证。
英文摘要
The statistics of current fluctuations has long been a central object of study in non-equilibrium physics. Most existing work has focused on one-time statistics, while their multi-time generalisation remains comparatively less explored. We address this gap by extending the fluctuating hydrodynamics framework of Macroscopic Fluctuation Theory (MFT) to study multi-time statistics in the non-stationary state of a diffusive system on an infinite line. For the simplest cases of a non-interacting lattice gas and hard-core Brownian point particles, we present explicit solution of the MFT leading to multi-time large-deviation statistics. For generic systems, the MFT is solved perturbatively, yielding explicit results for two-time correlations. These reveal that the connection between current fluctuations and fractional Brownian motion, previously observed for flat initial conditions, does not persist for step initial conditions. We independently verify these hydrodynamic results by solving the corresponding microscopic dynamics for the non-interacting gas and for the symmetric simple exclusion process. Additional confirmation comes from numerical simulations.
Comments50 pages, 5 figures, JSTAT Special Issue StatPhys29
