论文标题
Lorentzian熵和Olbert的$κ$分布
Lorentzian Entropies and Olbert's $κ$-distribution
论文作者
论文摘要
本说明得出了受Olbert分布（普遍的Lorentzian概率分布称为$κ$ - 分布）的各种形式的系统熵，这些熵经常被经常观察到，特别是在高温等离子体中。该系统中分区函数的一般表达也以类似于Boltzmann-Gibbs概率分布的形式，包括可能的指数高能截断。我们发现平均能量作为概率函数的表示，并提供了Olbert（Lorentzian）熵的隐式形式及其高温极限。获得了与状态的相空间密度的关系。然后，我们将熵作为概率的函数，这是统计力学基础和其Olbertian版本的表达式。洛伦兹系统通过内部集体相互作用引起的相关性，从而增加了熵。费米系统不遵守奥尔伯特的统计数据，而玻色系统可能在远离零的温度下可能。
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $κ$-distributions) which are frequently observed particularly in high temperature plasmas. The general expression of the partition function in such systems is given as well in a form similar to the Boltzmann-Gibbs probability distribution, including a possible exponential high energy truncation. We find the representation of the mean energy as function of probability, and provide the implicit form of Olbert (Lorentzian) entropy as well as its high temperature limit. The relation to phase space density of states is obtained. We then find the entropy as function of probability, an expression which is fundamental to statistical mechanics and here to its Olbertian version. Lorentzian systems through internal collective interactions cause correlations which add to the entropy. Fermi systems do not obey Olbert statistics, while Bose systems might at temperatures sufficiently far from zero.
