Single-particle velocity distributions of collisionless, steady-state plasmas must follow Superstatistics

The $q$-canonical ensemble as a consequence of Bayesian superstatistics

Superstatistics is a generalization of equilibrium statistical mechanics that describes systems in nonequilibrium steady states. Among the possible superstatistical distributions, the $q$-canonical ensemble (also known as Tsallis' statistics, and in plasma physics as Kappa distributions) is probably the most widely used, however the current explanations of its origin are not completely consistent. In this work it is shown that, under a Bayesian interpretation of superstatistics, the origin of the $q$-canonical ensemble can be explained as the superstatistical distribution with maximum Shannon-…

超统计作为受驱经典系统的热力学极限

Superstatistics as the thermodynamic limit of driven classical systems

本研究将超统计框架拓展至受外部能量涨落的经典系统，证明其热力学极限下的势能分布可用超统计描述，并通过Lennard-Jones晶体的分子动力学模拟验证了理论预测的正确性。

Fluctuating temperature outside superstatistics: thermodynamics of small systems

The existence of fluctuations of temperature has been a somewhat controversial topic in thermodynamics but nowadays it is recognized that they must be taken into account in small, finite systems. Although for nonequilibrium steady states superstatistics is becoming the \textit{de facto} framework for expressing such temperature fluctuations, some recent results put into question the idea of temperature as a phase space observable. In this work we present and explore the statistics that describes a part of an isolated system, small enough to have well-defined uncertainties in energy and tempera…

非平衡稳态等离子体中粒子关联产生的Kappa分布

Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas

本研究仅基于测试粒子与环境动能的依赖关系，从非平衡稳态理论推导出等离子体速度的Kappa分布，无需温度相关假设，拓宽了其应用范围，还提出用超统计逆温度特征描述更简便。

基本温度唯一决定超统计学（superstatistics）的有效性

Fundamental temperature exclusively determines the validity of superstatistics

针对超统计学并非普遍适用的问题，该研究给出非平衡稳态模型可由超统计学表示的充要条件，证明基本逆温度函数$β_F$唯一决定温度超统计分布的存在性。

A classification of nonequilibrium steady states based on temperature correlations

Although generalized ensembles have now been in use in statistical mechanics for decades, including frameworks such as Tsallis' nonextensive statistics and superstatistics, a classification of these generalized ensembles outlining the boundaries of validity of different families of models, is still lacking. In this work, such a classification is proposed in terms of supercanonical and subcanonical ensembles, according to a newly defined parameter, the inverse temperature covariance parameter $\mathcal{U}$. This parameter is non-negative in superstatistics (and is equal to the variance of the i…

Generalized superstatistics of nonequilibrium Markovian systems

The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff's diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes. The latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually. Then stationary probability as well as flux distributions are represented as some sums over the channels. The latter construction actually forms the superstatistical description, which, h…

冷暗物质晕中碰撞弛豫到普适准稳态吸引子的自洽准线性理论

A self-consistent quasilinear theory for collisionless relaxation to universal quasi-steady state attractors in cold dark matter halos

本文提出自洽准线性理论，在作用-角空间中推导准线性扩散方程，证明冷暗物质晕的 NFW 尖点、Einstein 核及 r^-1.5 尖点等普适密度轮廓均为碰撞弛豫的准稳态吸引子解。

无碰撞静电等离子体自洽演化产生的普适非热幂律分布函数

Universal non-thermal power-law distribution functions from the self-consistent evolution of collisionless electrostatic plasmas

通过准线性分析受驱动的无碰撞静电等离子体的Vlasov-Poisson方程，证明自洽演化是形成普适非热速度幂律尾部（$v^{-5}$）的关键机制。