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20 April 2024
 
  » arxiv » cond-mat/0110046

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The additivity of the pseudo-additive conditional entropy for a proper Tsallis' entropic index
T. Wada ; T. Saito ;
Date 2 Oct 2001
Journal Physica A 301 (2001) 284-290
Subject Statistical Mechanics | cond-mat.stat-mech
AbstractFor Tsallis’ entropic analysis to the time evolutions of standard logistic map at the Feigenbaum critical point, it is known that there exists a unique value $q^*$ of the entropic index such that the asymptotic rate $K_q equiv lim_{t o infty} {S_q(t)-S_q(0)/ t$ of increase in $S_q(t)$ remains finite whereas $K_q$ vanishes (diverges) for $q > q^* (q < q^*)$. We show that in spite of the associated whole time evolution cannot be factorized into a product of independent sub-interval time evolutions, the pseudo-additive conditional entropy $S_q(t|0) equiv {S_q(t)-S_q(0)}/ {1+(1-q)S_q(0)}$ becomes additive when $q=q^*$. The connection between $K_{q^*}$ and the rate $K’_{q^*} equiv S_{q^*}(t | 0) / t$ of increase in the conditional entropy is discussed.
Source arXiv, cond-mat/0110046
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