标题： 高斯随机动力学的正常和异常涨落关系 显示英文标题

标题： Normal and Anomalous Fluctuation Relations for Gaussian Stochastic Dynamics

摘要： 我们研究高斯随机系统产生异常扩散时的瞬态功涨落关系（FRs）。为此，我们采用朗之万方法，使用两种不同类型的加性噪声：(i) 内部噪声，其中第二类涨落-耗散关系（FDR II）成立，以及(ii)没有FDR II的外部噪声。对于内部噪声，我们证明FDR II的存在意味着第一类涨落-耗散关系（FDR I）的存在，这进而导致瞬态功FR的常规（正常）形式。对于由外部噪声驱动的系统，我们获得了常规FR的违反，我们称之为异常FR。我们在长时间极限下推导了它们，并展示了在中间时间FR中存在对数因子。我们还概述了可能的实验验证。 显示英文摘要

摘要： We study transient work Fluctuation Relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the Fluctuation-Dissipation Relation of the second kind (FDR II) holds, and (ii) external noise without FDR II. For internal noise we demonstrate that the existence of FDR II implies the existence of the Fluctuation-Dissipation Relation of the first kind (FDR I), which in turn leads to conventional (normal) forms of transient work FRs. For systems driven by external noise we obtain violations of normal FRs, which we call anomalous FRs. We derive them in the long-time limit and demonstrate the existence of logarithmic factors in FRs for intermediate times. We also outline possible experimental verifications.