标题： 异常动力学的涨落关系 显示英文标题

标题： Fluctuation relations for anomalous dynamics

摘要： 我们考虑生成异常扩散的通用动力学类型的工作涨落关系（FRs）：莱维飞行、长相关高斯过程和时间分数动力学。 通过结合朗之万和动力学方法，我们分别计算了在两个典型的非平衡情况下机械功和热力学功的概率分布：一个受到恒定力作用的粒子和一个在谐波势中被恒定力拖动的粒子。 我们检查了两种表现出超扩散的模型的瞬态FR，这些模型中不存在涨落-耗散关系，以及另外两种表现出次扩散的模型的瞬态FR，这些模型中存在涨落-耗散关系。 在前两种情况下，传统的瞬态FR没有被恢复，而在后两种情况下，它要么精确成立，要么在长时间极限下成立。 显示英文摘要

摘要： We consider work fluctuation relations (FRs) for generic types of dynamics generating anomalous diffusion: Levy flights, long-correlated Gaussian processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the probability distributions of mechanical and thermodynamical work in two paradigmatic nonequilibrium situations, respectively: a particle subject to a constant force and a particle in a harmonic potential dragged by a constant force. We check the transient FR for two models exhibiting superdiffusion, where a fluctuation-dissipation relation does not exist, and for two other models displaying subdiffusion, where there is a fluctuation-dissipation relation. In the two former cases the conventional transient FR is not recovered, whereas in the latter two it holds either exactly or in the long-time limit.