Quasi-equilibrium evolution in self-gravitating and long-range interacting systems

在像自引力系统这样的长程相互作用系统中，驰豫时间是相当长的。在长程相互作用系统的驰豫过程中，往往会出现与初始条件无关的准平衡态。我们讨论了从统计力学和N体粒子模拟两种分析方法来描述准平衡态的模型。证明了自引力系统中King模型的密度分布可用朗之万方程表示。结果表明，在负比热区，二维HMF模型中的准平衡态可以用非扩展熵的极大值来拟合。另一方面，在正比热区，我们不能很好地拟合准平衡态和非扩展熵的最大态。

In long-range interacting systems such as self-gravitating system, it is known that relaxation time is quite long. Then during relaxation process in the long-range interacting systems, quasi-equilibrium state which is independent of initial conditions often appears. We discuss the models which can describe the quasi-equilibrium state with both analytic methods from statistical mechanics and N-body particles simulation. Then we showed that the density distribution of King model is represented by using Langevin equation in self-gravitating system. We showed that, in negative specific heat region, the quasi-equilibrium state in 2-dimensional HMF model can be fitted by maximum state of non-extensive entropy. On the other hand, in positive specific heat region, we cannot fit the quasi-equilibrium state with maximum state of non-extensive entropy.