广义统计的参数及其相互关系

Parameters of generalized statistics and their interrelationship

利用广义玻尔兹曼方程、广义统计的分布函数和熵函数,推导了Tsallis非广延性熵、κ熵、Abe熵以及更为广泛的双参数广义熵函数中参数的物理意义,分析了不同广义统计之间的关系以及各自适用的系统。其中,Tsallis熵的参数q、κ熵中的参数κ都代表了系统温度梯度的大小,即系统偏离平衡态的程度。Tsallis统计下,系统温度梯度和外场力是平行的;而κ统计下,系统温度梯度和外场力是垂直的。Abe熵中的参数qA也可以表示系统温度梯度和外场力之间的关系。

The physical meaning of the parameter in Tsallis nonextensive entropy, K entropy, Abe entropy and more generalized two-parameter entropy is studied by adopting generalized Bohzmann equations, generalized statistics distri- bution functions and entropies. The relation among different generalized statistics and the field that can be applied for is also studied. Parameter q in Tsallis entropy and K in K entropy represent the spatial inhomogeneity of temperature. They also mean the degree of the system deviating from the equilibrium. The temperature gradient of the system and external force are parallel in Tsallis statistics, while they are vertical in K statistics. Parameter qA in Abe entropy also shows the relationship between the temperature gradient and external force.