发表机构
Institute for Nuclear Research（核物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展随机路径空间热力学，引入边界与相对泛函，研究非对称漂移及阶梯势下Ornstein-Uhlenbeck过程的涨落，提出修正涨落定理并应用于离子通道建模。
AI 中文摘要
本文通过系统地扩展热力学变量空间，引入随机过程的边界泛函和相对泛函谱，扩展了随机路径空间热力学的形式体系。推广了预印本arXiv:2607.24078和arXiv:2609.08477中引入的方法，我们研究了一维Ornstein-Uhlenbeck过程的涨落统计，该过程具有非对称线性漂移和原点处的阶梯惩罚势，用于模拟分子布朗马达的等待阶段。利用Feynman-Kac形式和抛物柱面理论，构建了基于割线法匹配对数导数的数值方案。获得了有效哈密顿量的高精度本征值，这些本征值定义了累积量生成函数。我们针对耗散半平面中系统在固定积分占据时间下的共轭漂移电流，提出了修正的Gallavotti-Cohen型路径空间涨落定理。阐明了新变量的物理和热力学意义。将“停留时间”和“积分电流”泛函的组合应用于描述对机械或电刺激敏感的离子通道。
英文摘要
This paper extends the formalism of stochastic path-space thermodynamics by systematically expanding the space of thermodynamic variables with a spectrum of boundary and relative functionals of random processes. Generalizing the approaches introduced in preprints arXiv:2607.24078 and arXiv:2609.08477, we investigate the fluctuation statistics of a one-dimensional Ornstein-Uhlenbeck process with an asymmetric linear drift and a step penalty potential at the origin, which models the waiting phase of a molecular Brownian motor. Utilizing the Feynman-Kac formalism and the parabolic cylinder theory, a numerical scheme based on matching logarithmic derivatives via the secant method is constructed. A high-precision eigenvalues of the effective Hamiltonian is obtained, which define the cumulant generating function. We formulate a modified path-space fluctuation theorem of the Gallavotti-Cohen type for the conjugate drift current at a fixed integral occupation time of the system in the dissipative half-plane. The physical and thermodynamic significance of the new variables is elucidated. A combination of "residence time" and "integral current" functionals is applied to describe an ion channel sensitive to mechanical or electrical stimuli.
Comments23 pages, 3 figures. This work extends and generalizes the trajectory functional approach introduced in preprints arXiv:2607.24078 and arXiv:2609.08477 by incorporating relative path-space invariants and establishing a modified strong-drift fluctuation theorem
