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Generalized Entropy Production in Collisionless Plasma Flows and Turbulence
Physical Review X ( IF 12.5 ) Pub Date : 2022-07-18 , DOI: 10.1103/physrevx.12.031011
Vladimir Zhdankin

Collisionless plasmas exhibit nonthermal and anisotropic particle distributions after being energized; as a consequence, they enter a state of low Boltzmann-Gibbs (BG) entropy relative to the thermal state. The Vlasov equations predict that in a collisionless plasma with closed boundaries, BG entropy is formally conserved, along with an infinite set of other Casimir invariants; this provides a seemingly strong constraint that may explain how plasmas maintain low entropy. Nevertheless, it is commonly believed that entropy production is enabled by phase mixing or nonlinear entropy cascades. The question of whether such anomalous entropy production occurs, and of how to characterize it quantitatively, is a fundamental problem in plasma physics. We construct a new theoretical framework for characterizing entropy production (in a generalized sense) based on a set of ideally conserved dimensional quantities derived from the Casimir invariants; these are referred to as the “Casimir momenta,” and they generalize the BG entropy. The growth of the Casimir momenta relative to the average particle momentum indicates entropy production. We apply this framework to quantify entropy production in particle-in-cell simulations of laminar flows and turbulent flows driven in relativistic plasma, where efficient nonthermal particle acceleration is enabled. We demonstrate that a large amount of anomalous entropy is produced by turbulence despite nonthermal features. The Casimir momenta grow to cover a range of energies in the nonthermal tail of the distribution, and we correlate their growth with spatial structures. These results have implications for reduced modeling of nonthermal particle acceleration and for diagnosing irreversible dissipation in collisionless plasmas such as the solar wind and Earth’s magnetosphere. Dimensional representations of generalized entropy analogous to the Casimir momenta may be useful for other problems in statistical physics.

中文翻译:

无碰撞等离子体流和湍流中的广义熵产生

无碰撞等离子体在通电后呈现出非热和各向异性的粒子分布;因此,它们进入相对于热态的低玻尔兹曼-吉布斯 (BG) 熵状态。Vlasov 方程预测,在具有封闭边界的无碰撞等离子体中,BG 熵和其他无限的卡西米尔不变量集在形式上是守恒的;这提供了一个看似强大的约束,可以解释等离子体如何保持低熵。然而,通常认为熵的产生是通过相位混合或非线性熵级联实现的。是否会发生这种异常熵产生以及如何对其进行定量表征的问题是等离子体物理学中的一个基本问题。我们构建了一个新的理论框架,用于基于从卡西米尔不变量派生的一组理想守恒的维度量来表征熵产生(广义上);这些被称为“卡西米尔动量”,它们概括了 BG 熵。卡西米尔动量相对于平均粒子动量的增长表明熵的产生。我们应用该框架来量化在相对论等离子体中驱动的层流和湍流的粒子单元模拟中的熵产生,其中启用了有效的非热粒子加速。我们证明,尽管有非热特征,但湍流会产生大量异常熵。卡西米尔动量增长到覆盖分布的非热尾部中的一系列能量,我们将它们的增长与空间结构联系起来。这些结果对减少非热粒子加速度的建模和诊断无碰撞等离子体(如太阳风和地球磁层)中的不可逆耗散具有重要意义。类似于卡西米尔动量的广义熵的维数表示可能对统计物理学中的其他问题有用。
更新日期:2022-07-18
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