When non-extensive entropy becomes extensive

Abstract

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 $q^{\ast }$. We propose an alternative constraint of obtaining the proper entropic index $q^{\ast }$ that the non-additive conditional entropy becomes additive if and only if $q=q^{\ast }$ 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 $q\ne 1$.

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

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