Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive.

ABSTRACT: Phase space can be constructed for N equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy S(BG) identical with -k Sigma(i) p(i) ln p(i) to be extensive, i.e., S(BG)(N) proportional, variant N for N --> infinity. In particular, if they are independent, S(BG) is strictly additive, i.e., S(BG)(N) = NS(BG)(1), for allN. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy S(q) identical with k[1 - Sigma(i) p(q)(i)]/(q - 1) (with S(1) = S(BG)) for some special value of q not equal 1 to be the one which is extensive [i.e., S(q)(N) proportional, variant N for N --> infinity]. Another concept which is relevant is s

SUBMITTER: Tsallis C 

PROVIDER: S-EPMC1266086 | biostudies-literature | 2005 Oct

REPOSITORIES: biostudies-literature