Anomalous behavior of q-averages in nonextensive statistical mechanics
Anomalous behavior of q-averages in nonextensive statistical mechanics
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DOI：
10.1088/1742-5468/2009/07/p07027
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发表时间：
2009-06
期刊：
影响因子：
--
通讯作者：
S. Abe
中科院分区：
文献类型：
--
作者：
S. Abe
平均的广义定义，称为q-平均，广泛应用于非广延统计力学领域。然而，最近有人指出，在概率分布的特定变形下，这样的平均值可能会表现出非物理的行为。在此，讨论并澄清以下三个问题。首先，考虑的变形是物理的，可以通过实验实现。其次，从热统计学的观点来看，q-平均在有限和无限离散系统中都是不稳定的。第三，将讨论简单地推广到连续系统会忽略一点，应该使用比L1范数更好的范数来测量两个概率分布之间的距离。因此，q-平均值的稳定性并不是在所有情况下都成立的。
A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysically under specific deformations of probability distributions. Here, the following three issues are discussed and clarified. Firstly, the deformations considered are physical and may be realized experimentally. Secondly, in view of the thermostatistics, the q-average is unstable in both finite and infinite discrete systems. Thirdly, a naive generalization of the discussion to continuous systems misses a point, and a norm better than the L1-norm should be employed for measuring the distance between two probability distributions. Consequently, stability of the q-average is shown not to be established in all of the cases.