AI 中文总结
该研究用基于共形变换的分解法推导一维非线性广义朗之万方程，采用改进的 Mori-Zwanzig 方法并结合离散洛厄纳演化重新表述涨落耗散关系，通过数值模拟得到能量耗散标度律，还用洛厄纳熵估计有色噪声环境中的正则系综。
AI 中文摘要
在本研究中，使用基于弦向洛厄纳方程控制的共形变换的分解方法，展示了一维非线性广义朗之万方程的形式推导。采用了一种改进的 Mori-Zwanzig 方法，其算子由离散洛厄纳演化导出的算子替代。通过这种方法，利用受共形映射影响的数学术语重新表述了不同类型的涨落耗散关系（FDR）。针对模拟细胞迁移实验的记忆核进行数值模拟，以获得两种 FDR 共有的能量耗散特定标度律。此外，在整个理论分析中，洛厄纳熵的概念用于估计有色噪声环境中的正则系综。
英文摘要
In this study, the formal derivation of a one-dimensional nonlinear generalized Langevin equation is demonstrated using a decomposition method based on the conformal transformation governed by the chordal Loewner equation. Here, we used a modified Mori-Zwanzig method whose operator is substituted by that is derived from the discrete Loewner evolution. By this approach, the different types of fluctuation-dissipation relation (FDR) were reformulated using mathematical terms affected by the conformal maps. Dealing with a memory kernel that models the cell migration experiment, the numerical simulation was performed to obtain the specific scaling law of energy dissipation that is common among the two obtained types of FDRs. In addition, the concept of Loewner entropy is used for the estimation of the canonical ensemble in the colored noise environment throughout the theoretical analyses.
Comments12 pages, 2 figures
