  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 $q \ne 1$.
