Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China.
Phys Rev E. 2019 Nov;100(5-1):052149. doi: 10.1103/PhysRevE.100.052149.
The generalized Einstein relation (GER) for nonergodic processes is investigated within the framework of the generalized Langevin equation. The conditions for anomalous relaxation such as long-tail decay and non-vanishing velocity autocorrelation function (VAF) are proposed and distinguished. For the stationary nonergodic process, if the initial preparation of the particle velocity is non-thermal, an asymptotic GER occurs in a departure from the usual result. It is shown that the GER holding is a necessary condition rather than a full condition for the system being close to equilibrium. For the nonergodic process of the second type due to cutoff of high frequencies, the VAF oscillates with time, the GER holds but the equilibrium fails in the long-time limit. Applications to some practical examples confirm the present theoretical findings.
本文在广义朗之万方程的框架下研究了非遍历过程的广义爱因斯坦关系（GER）。提出并区分了反常弛豫的条件，如长尾衰减和非零速度自相关函数（VAF）。对于稳定的非遍历过程，如果粒子速度的初始制备是非热的，则会出现偏离通常结果的渐近 GER。结果表明，GER 的成立是系统接近平衡的必要条件，而不是充分条件。对于由于高频截止引起的第二类非遍历过程，VAF 随时间振荡，GER 成立，但在长时间极限下平衡失效。对一些实际例子的应用证实了本文的理论结果。
