Ourabah Kamel
Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, Boite Postale 32, El Alia, Algiers 16111, Algeria.
Phys Rev E. 2024 Jan;109(1-1):014127. doi: 10.1103/PhysRevE.109.014127.
Distributions that deviate from equilibrium predictions are commonly observed across a broad spectrum of systems, ranging from laboratory experiments to astronomical phenomena. These distributions are generally regarded as a manifestation of a quasiequilibrium state and can very often be represented as a superposition of statistics, i.e., superstatistics. The underlying idea in this methodology is that the nonequilibrium system consists of a collection of smaller subsystems that remain infinitely close to equilibrium. This procedure has been effectively implemented in a kinetic setting, but thus far, only in the collisionless regime, limiting its scope of application. In this paper, we address the effect of collisions on the relaxation process and time evolution of superstatistical systems. After confronting the superstatistical distributions with experimental and simulation data, relevant to our analysis, we first study the effect of superstatistics on entropy. We explicitly show that, in the absence of long-range interactions, the extensivity of entropy is preserved, albeit influenced by the specific class of temperature fluctuations. Then, we examine how collisions drive the system towards a global equilibrium state, characterized by a maximum entropy, by employing the relaxation time approximation. This allows us to define a dynamical version of superstatistics, characterized by a singular time-varying parameter q(t), which undergoes a continuous evolution towards equilibrium. We show how this approach enables the determination of the evolution of the underlying temperature distribution under the influence of collisions, which act as stochastic forces, gradually narrowing the temperature distribution over time.
偏离平衡预测的分布在广泛的系统中普遍存在，从实验室实验到天文现象。这些分布通常被视为准平衡态的一种表现，并且常常可以表示为统计量的叠加，即超统计。这种方法的基本思想是，非平衡系统由一组无限接近平衡的较小子系统组成。这个过程已经在动力学环境中有效地实现了，但到目前为止，仅在无碰撞 regime 中实现，限制了其应用范围。在本文中，我们讨论了碰撞对超统计系统的弛豫过程和时间演化的影响。在用与我们的分析相关的实验和模拟数据验证了超统计分布之后，我们首先研究了超统计对熵的影响。我们明确表明，在没有长程相互作用的情况下，熵的广延性得以保留，尽管受到特定类别的温度涨落的影响。然后，我们通过采用弛豫时间近似来研究碰撞如何驱动系统趋向于以最大熵为特征的全局平衡态。这使我们能够定义一种超统计的动力学版本，其特征是一个奇异的时变参数 q(t)，它朝着平衡态进行连续演化。我们展示了这种方法如何能够确定在作为随机力的碰撞影响下基础温度分布的演化，碰撞随着时间的推移逐渐使温度分布变窄。
