McComas David J, Livadiotis George, Sarlis Nicholas V
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA.
Physics Department, National and Kapodistrian University of Athens, Panepistimiopolis, 15784 Athens, Greece.
Entropy (Basel). 2025 Mar 31;27(4):375. doi: 10.3390/e27040375.
Kappa distributions, their statistical framework, and their thermodynamic origin describe systems with correlations among their particle energies, residing in stationary states out of classical thermal equilibrium/space plasmas, from solar wind to the outer heliosphere, are such systems. We show how correlations from long-range interactions compete with collisions to define the specific shape of particle velocity distributions, using a simple numerical experiment with collisions and a variable amount of correlation among the particles. When the correlations are turned off, collisions drive any initial distribution to evolve toward equilibrium and a Maxwell-Boltzmann (MB) distribution. However, when some correlation is introduced, the distribution evolves toward a different stationary state defined by a kappa distribution with some finite value of the thermodynamic kappa κ (where κ→∞ corresponds to a MB distribution). Furthermore, the stronger the correlations, the lower the κ value. This simple numerical experiment illuminates the role of correlations in forming stationary state particle distributions, which are described by kappa distributions, as well as the physical interpretation of correlations from long-range interactions and how they are related to the thermodynamic kappa.
κ分布、其统计框架及其热力学起源描述了粒子能量之间存在相关性的系统，这些系统处于经典热平衡之外的稳态，从太阳风到外日球层的空间等离子体就是这样的系统。我们通过一个简单的包含碰撞以及粒子间可变相关量的数值实验，展示了长程相互作用产生的相关性如何与碰撞相互竞争，从而确定粒子速度分布的具体形状。当相关性被关闭时，碰撞会驱使任何初始分布朝着平衡态和麦克斯韦-玻尔兹曼（MB）分布演化。然而，当引入一些相关性时，分布会朝着由具有有限热力学κ值的κ分布所定义的不同稳态演化（其中κ→∞对应于MB分布）。此外，相关性越强，κ值越低。这个简单的数值实验阐明了相关性在形成由κ分布描述的稳态粒子分布中的作用，以及长程相互作用相关性的物理解释，以及它们与热力学κ是如何相关的。
