In:
Journal of Mathematical Physics, AIP Publishing, Vol. 48, No. 11 ( 2007-11-01)
Abstract:
The q-sum x⊕qy≡x+y+(1−q)xy (x⊕1y=x+y) and the q-product x⊗qy≡[x1−q+y1−q−1]1∕(1−q) (x⊗1y=xy) emerge naturally within nonextensive statistical mechanics. We show here how they lead to two-parameter (namely, q and q′) generalizations of the logarithmic and exponential functions (noted, respectively, lnq,q′x and eq,q′x), as well as of the Boltzmann-Gibbs-Shannon entropy SBGS≡−k∑i=1Wpilnpi (noted Sq,q′). The remarkable properties of the (q,q′)-generalized logarithmic function make the entropic form Sq,q′≡k∑i=1Wpilnq,q′(1∕pi) satisfy, for large regions of (q,q′), important properties such as expansibility, concavity, and Lesche stability, but not necessarily composability.
Type of Medium:
Online Resource
ISSN:
0022-2488
,
1089-7658
Language:
English
Publisher:
AIP Publishing
Publication Date:
2007
detail.hit.zdb_id:
1472481-9
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