Generalized thermostatistics based on deformed exponential and logarithmic functions
Generalized thermostatistics based on deformed exponential and logarithmic functions
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基于变形指数和对数函数的广义恒温统计
DOI：
10.1016/j.physa.2004.03.074
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发表时间：
2003
影响因子：
3.3
通讯作者：
J. Naudts
中科院分区：
文献类型：
--
作者：
J. Naudts
均分定理指出，温度的倒数等于态密度的对数导数。这个关系可以通过引入一个包含递增正函数φ（x）的比例因子来推广。结果表明，这一假设导致玻尔兹曼-吉布斯形式的平衡分布的指数函数所取代的变形指数函数。用这种方法，我们得到了作者以前介绍过的广义热统计学的一种形式。结果表明，Tsallis的热统计学，稍加修改，是这种形式主义的最明显的例子，并对应于选择φ（x）=xq。
The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function φ(x). It is shown that this assumption leads to an equilibrium distribution of the Boltzmann–Gibbs form with the exponential function replaced by a deformed exponential function. In this way one obtains a formalism of generalized thermostatistics introduced previously by the author. It is shown that Tsallis’ thermostatistics, with a slight modification, is the most obvious example of this formalism and corresponds with the choice φ(x)=xq.