泛公理-非广延统计量的热力学自洽性
On thermodynamic self-consistency of generic axiomatic-nonextensive statistics
摘要：
一般公理非广延统计的特点是两个渐近性质，每一个被分配的标度函数，其特征在于c和d的第一和第二标度性质，分别制定在一个巨正则系综有限体积的热力学极限。研究了强子共振态相对论性理想气体的热力学性质。结果表明，该统计量满足平衡态热力学的要求。阐明了热力学自洽性的基本方面。给出了不同碰撞能量和碰撞系统下最中心碰撞中测量的各种横向动量分布的统计拟合的解析表达式。估计的冻出温度和化学势和c和d的确定。前者被发现兼容的参数推导出的玻尔兹曼-吉布斯（BG）统计（广泛），而后者是指通用nonextensivity。由此产生的等价类（c，d）与拉伸指数相关联，其中Lambert函数达到其渐近稳定性。在某些测量中，所得到的非广延熵是由广延熵线性组成的。除了功率缩放，颗粒比率和产量是突出颗粒生产是否广泛发生的极好数量。不同的粒子比和产率测量的STAR实验在200，62.4和7.7 GeV的中心碰撞适合这种新的方法。我们发现c和d都<1，即既不是BG-型统计量，也不是Tsallis-型统计量，而是（c，d）-熵，其中朗伯函数呈指数增长。我们的结论是，在STAR能量的粒子生产可能是一个非广泛的过程，但不一定BG或Tsallis类型。
英文摘要：
Generic axiomatic-nonextensive statistics characterized by two asymptotic properties, to each of them a scaling function is assigned, characterized by c and d for first and second scaling property, respectively, is formulated in a grand-canonical ensemble with finite volume in the thermodynamic limit. The thermodynamic properties of a relativistic ideal gas of hadron resonances are studied. It is found that this generic statistics satisfies the requirements of the equilibrium thermodynamics. Essential aspects of thermodynamic self-consistency are clarified. Analytical expressions are proposed for the statistical fits of various transverse momentum distributions measured in most-central collisions at different collision energies and colliding systems. Estimations for the freezeout temperature and chemical potential and both c and d are determined. The earlier are found compatible with the parameters deduced from Boltzmann-Gibbs (BG) statistics (extensive), while the latter refer to generic nonextensivity. The resulting equivalence class (c,d) is associated to stretched exponentials, where Lambert function reaches its asymptotic stability. In some measurements, the resulting nonextensive entropy is linearly composed of extensive entropies. Apart from power-scaling, the particle ratios and yields are excellent quantities to highlighting whether the particle production takes place, (non)extensively. Various particle ratios and yields measured by the STAR experiment in central collisions at 200, 62.4 and 7.7 GeV are fitted to this novel approach. We found that both c and d<1, i.e. referring to neither BG- nor Tsallis-type statistics, but to (c,d)-entropy, where Lambert functions exponentially raise. We conclude that the particle production at STAR energies is likely a nonextensive process but not necessarily BG or Tsallis type.
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