Sarlis Nicholas V, McComas David J, Livadiotis George
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 Jun 17;27(6):646. doi: 10.3390/e27060646.
McComas et al. (2025) introduced a numerical experiment, where ordinary uncorrelated collisions between collision pairs are followed by other, controlled (correlated) collisions, shedding light on the emergence of kappa distributions through particle correlations in space plasmas. We extend this experiment by introducing correlations indicating that (i) when long-range correlations are interwoven with collision pairs, the resulting thermodynamic kappa are described as that corresponding to an 'interatomic' potential interaction among particles; (ii) searching for a closer description of heliospheric plasmas, we found that pairwise short-range correlations are sufficient to lead to appropriate values of thermodynamic kappa, especially when forming correlated clusters; (iii) multi-particle correlations do not lead to physical stationary states; finally, (iv) an optimal model arises when combining all previous findings. In an excellent match with space plasmas observations, the thermodynamic kappa that describes the stationary state at which the system is stabilized behaves as follows: (a) When correlations are turned off, kappa is turning toward infinity, indicating the state of classical thermal equilibrium (Maxwell-Boltzmann distribution), (b) When collisions are turned off, kappa is turning toward the anti-equilibrium state, the furthest state from the classical thermal equilibrium (-5 power-law phase-space distribution), and (c) the finite kappa values are generally determined by the competing factor of collisions and correlations.
麦科马斯等人（2025年）介绍了一项数值实验，其中碰撞对之间普通的不相关碰撞之后是其他受控（相关）碰撞，通过空间等离子体中的粒子相关性揭示了kappa分布的出现。我们通过引入相关性来扩展这项实验，结果表明：（i）当长程相关性与碰撞对交织在一起时，由此产生的热力学kappa被描述为对应于粒子间“原子间”势相互作用的kappa；（ii）为了更精确地描述日球层等离子体，我们发现成对的短程相关性足以导致热力学kappa的适当值，特别是在形成相关簇时；（iii）多粒子相关性不会导致物理稳态；最后，（iv）当结合所有先前的发现时会出现一个最优模型。与空间等离子体观测结果完美匹配的是，描述系统稳定时稳态的热力学kappa表现如下：（a）当相关性关闭时，kappa趋向于无穷大，表明处于经典热平衡状态（麦克斯韦-玻尔兹曼分布）；（b）当碰撞关闭时，kappa趋向于反平衡状态，即离经典热平衡最远的状态（-5幂律相空间分布）；（c）有限的kappa值通常由碰撞和相关性的竞争因素决定。
