发表机构
Universidad Andres Bello（安第斯贝尔托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用杰恩斯最大熵原理，以动能对数矩为约束，从单粒子动能数据中重建超统计的逆温度分布，并能区分三个普适类。
AI 中文摘要
超统计框架可用于将非麦克斯韦单粒子速度分布描述为麦克斯韦分布的混合，其中权重由与逆温度 $\eta = 1/(k_B T)$ 相关的概率密度施加。$\eta$ 的典型模型选择包括伽马分布、逆伽马分布和对数正态分布，有时被称为超统计的普适类。然而，给定一组观测到的速度，没有直接方法来确定潜在的温度分布，因为温度本身不是相空间可观测量，并且数值上反转拉普拉斯变换是不可靠的过程。在这项工作中，我们表明，通过使用动能的对数矩作为约束，杰恩斯最大熵原理可用于从数据中成功重建逆温度分布。尽管在 $\eta$ 的相同均值和方差下，三个普适类的动能分布几乎无法区分，但该方法能正确区分它们。
英文摘要
The framework of superstatistics can be used to describe non-Maxwellian single-particle velocity distributions as mixtures of Maxwellian distributions, where the weight is imposed by a probability density associated to the inverse temperature $β= 1/(k_B T)$. Among the typical model choices for $β$ are gamma, inverse gamma and lognormal distributions, sometimes called the universality classes of superstatistics. Given a set of observed velocities, however, there is no direct method to determine the underlying temperature distribution, as temperature itself is not a phase-space observable, and numerically inverting the Laplace transform is an unreliable process. In this work, we show that Jaynes' principle of maximum entropy can be used to successfully reconstruct the inverse temperature distribution from data, by using the logarithmic moments of the kinetic energy as constraints. Although the kinetic energy distributions for the three universality classes are almost indistinguishable at the same mean and variance of $β$, the method correctly discriminates between them.
