We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e. entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow and temperature as the local distribution. First, we consider a form previously employed by Kaufmann & Paterson (J. Geophys. Res., vol. 114, 2009, A00D04), assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.

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基于动力学熵的非麦克斯韦分布函数测量：理论与模拟

我们研究了等离子体中分布函数的非麦克斯韦分布的基于动力学熵的测量，即局部分布函数与具有与局部分布相同的密度、体积流量和温度的相关麦克斯韦分布函数的偏离的基于熵的测量. 首先，我们考虑考夫曼和帕特森以前使用的一种形式（J.地球物理学。水库。, 卷。114, 2009, A00D04)，评估其性质并推导等效形式。为了提供对它的定量理解，我们推导出三种常见的非麦克斯韦等离子体分布函数的解析表达式。我们表明，这种非麦克斯韦度量存在一些不良特征，包括它可以在各种物理极限下发散，并阐明了发散的原因。然后，我们引入了一种基于速度-空间动熵密度的新的基于动能熵的非麦克斯韦度量，它具有有意义的物理解释并且不会发散。我们使用二维反平行磁重联的无碰撞粒子细胞模拟来评估基于动力学熵的非麦克斯韦测量。我们表明，非零非麦克斯韦区域与磁重联期间发生的动力学过程有关。我们还表明，模拟的非麦克斯韦式与对类似于分析计算的分布的预测相当吻合。这些结果对应用很重要，因为非麦克斯韦性可用于识别动力学尺度物理区域或等离子体中增加的耗散。