When non-extensive entropy becomes extensive

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Tsallis' non-extensive entropy Sq 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 ≠ 1.