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• W1997414622 abstract "Phase space can be constructed for $N$ equal and distinguishable subsystems that could be (probabilistically) either {it weakly} (or {it locally}) correlated (e.g., independent, i.e., uncorrelated), or {it strongly} (or {it globally}) correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy $S_{BG} equiv -k sum_i p_i ln p_i$ to be {it extensive}, i.e., $S_{BG}(N)propto N $ for $N toinfty$. In particular, if they are independent, $S_{BG}$ is {it strictly additive}, i.e., $S_{BG}(N)=N S_{BG}(1), forall N$. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy $S_qequiv k [1- sum_i p_i^q]/(q-1)$ (with $S_1=S_{BG}$) for some special value of $qne1$ to be the one which extensive (i.e., $S_q(N)propto N $ for $N toinfty$)." @default.
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• W1997414622 creator A5003583590 @default.
• W1997414622 creator A5017032627 @default.
• W1997414622 creator A5051451815 @default.
• W1997414622 date "2005-10-17" @default.
• W1997414622 modified "2023-10-15" @default.
• W1997414622 title "Asymptotically scale-invariant occupancy of phase space makes the entropy <i> S _q </i> extensive" @default.
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• W1997414622 doi "https://doi.org/10.1073/pnas.0503807102" @default.
• W1997414622 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/1266086" @default.
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