When non-extensive entropy becomes extensive

Details When non-extensive entropy becomes extensive When non-extensive entropy becomes extensive

2001-05-22

arxiv.org/abs/cond-mat/0105419v1

Physica A 301 (2001) 284-290

Physics

Condensed Matter

Statistical Mechanics

8 pages, no figure, LaTeX2e, elsart. submit to Physica A

Scientific paper

10.1016/S0378-4371(01)00400-9

Tsallis' non-extensive entropy $S_q$ enables us to treat both a power and exponential evolutions of underlying microscopic dynamics on equal footing by adjusting the variable entropic index $q$ to proper one $q^*$. We propose an alternative constraint of obtaining the proper entropic index $q^*$ that the non-additive conditional entropy becomes additive if and only if $q=q^*$ in spite of that the associated system cannot be decomposed into statistically independent subsystems. Long-range (time) correlation expressed by $q$-exponential function is discussed based on the nature that $q$-exponential function cannot be factorized into independent factors when $q \ne 1$.

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