排斥粒子耗散系统的一般连续统方法
General continuum approach for dissipative systems of repulsive particles
摘要：
我们提出了一个通用的粗粒化方法，推导出一个连续性方程，描述任何耗散系统的排斥粒子相互作用，通过短程电位。在我们的方法中，粒子-粒子相关性的影响被纳入到整体的能量平衡，并得到一个非线性扩散方程来表示过阻尼动力学。特别是，当排斥相互作用势是一个短程幂律，我们的方法揭示了一个独特的对应粒子-粒子能量和广义热统计Tsallis的任何非正值的熵指数q。我们的方法也可以应用到超导涡流和复杂的等离子体，粒子粒子的相关性在低浓度下是明显的微观模型。由此产生的连续描述这些物理系统的微观动力学行为提供了阐明和有用的见解。通过与分子动力学模拟的比较，证明了我们的方法的一致性。
英文摘要：
We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle correlations is incorporated to the overall balance of energy, and a non-linear diffusion equation is obtained to represent the overdamped dynamics. In particular, when the repulsive interaction potential is a short-ranged power-law, our approach reveals a distinctive correspondence between particle-particle energy and the generalized thermostatistics of Tsallis for any non-positive value of the entropic index q. Our methodology can also be applied to microscopic models of superconducting vortices and complex plasma, where particle-particle correlations are pronounced at low concentrations. The resulting continuum descriptions provide elucidating and useful insights on the microdynamical behavior of these physical systems. The consistency of our approach is demonstrated by comparison with molecular dynamics simulations.
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