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When non-extensive entropy becomes extensive

Wada Tatsuaki·Saito Takeshi
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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 $q^*$. 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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Wada Tatsuaki, Saito Takeshi. 2001-05-22. When non-extensive entropy becomes extensive. https://doi.org/10.1016/s0378-4371(01)00400-9

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