Self-similarity degree of deformed statistical ensembles

被引:4
|
作者
Olemskoi, A. I. [1 ]
Vaylenko, A. S. [2 ]
Shuda, I. A. [2 ]
机构
[1] Natl Acad Sci Ukraine, Inst Appl Phys, UA-40030 Sumy, Ukraine
[2] Sumy State Univ 2, UA-40007 Sumy, Ukraine
关键词
Self-similarity; Dilatation; Jackson derivative; Homogeneous function; THERMOSTATISTICS; ENTROPIES; SETS;
D O I
10.1016/j.physa.2009.01.024
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider self-similar statistical ensembles with the phase space whose volume is invariant under the deformation that squeezes (expands) the coordinate and expands (squeezes) the momentum. The related probability distribution function is shown to possess a discrete symmetry with respect to manifold action of the Jackson derivative to be a homogeneous function with a self-similarity degree q fixed by the condition of invariance under (n + 1)-fold action of the related dilatation operator. Ill slightly deformed phase space, we find the homogeneous function is defined with the linear dependence at n = 0, whereas the self-similarity degree equals the gold mean at n = 1, and q -> n in the limit it n -> infinity. Dilatation of the homogeneous function is shown to decrease the self-similarity degree q at it > 0. (c) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码:1929 / 1938
页数:10
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