When non-extensive entropy becomes extensive

Tsallis’ non-extensive entropy S−q enables us to treat both power and exponential evolutions of underlying microscopic dynamics on an 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 the fact that the associated system cannot be decomposed into statistically independent subsystems. Long-range (time) correlation expressed by the q-exponential function is discussed based on the nature that the q-exponential function cannot be factorized into independent factors when q≠1.