Up-Hill Diffusion, Creation of Density Gradients: Entropy Measure for Systems with Topological Constraints
Up-Hill Diffusion, Creation of Density Gradients: Entropy Measure for Systems with Topological Constraints
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上山扩散，密度梯度的创建：具有拓扑约束的系统的熵测量
DOI：
10.1103/physreve.93.062140
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发表时间：
2016
影响因子：
2.4
通讯作者：
N. Sato and Z. Yoshida
中科院分区：
文献类型：
--
作者：
Kajigaya Toru;Kunikawa Keita;Keita Kunikawa;N. Sato and Z. Yoshida;N. Sato and Z. Yoshida;浦野綾子;國川慶太;國川慶太;浦野綾子;N. Sato and Z. Yoshida
从统计平均值中得出任何不平凡的结构总是有某种约束的。作为玻尔兹曼分布的缩影，能量守恒往往是作用于机械系统的主要约束。这里我们研究一种不同的类型：施加在“空间”上的拓扑约束。这样的约束从泊松算符的零空间中出现，它将能量梯度与相空间速度联系起来，并表现为一个绝热不变量，改变了统计力学核心中保留的相空间体积。建立在扭曲的不变度量基础上的正确的熵度量符合热力学第二定律。相反的行为(减少熵和负熵产生)在任意坐标下出现。求出了旋转刚体系综解。然后将该理论应用于磁层中的上坡扩散。
It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here we investigate a different type: the topological constraint imposed on “space.” Such a constraint emerges from the null space of the Poisson operator linking an energy gradient to phase space velocity and appears as an adiabatic invariant altering the preserved phase space volume at the core of statistical mechanics. The correct measure of entropy, built on the distorted invariant measure, behaves consistently with the second law of thermodynamics. The opposite behavior (decreasing entropy and negative entropy production) arises in arbitrary coordinates. An ensemble of rotating rigid bodies is worked out. The theory is then applied to up-hill diffusion in a magnetosphere.