Nota de FísicaPublicado
Special scale-invariant occupancy of phase space makes the entropy additive
C. Tsallis; Murray Gell-Mann; Yuzuru Sato
Datos de la publicación
- Autores
- C. Tsallis; Murray Gell-Mann; Yuzuru Sato
- Tipo
- Nota de Física
- Estado
- Publicado
- Fecha de publicación
- 14/07/2010
- Descripción
- Phase space can be constructed for $N$ equal subsystems that could be (probabilistically) either independent or correlated. If they are independent, Boltzmann-Gibbs entropy $S_{BG} \equiv -k \sum_i p_i \ln p_i$ is {\it strictly additive} in the sense that $S_{BG}(N)=N S_{BG}(1)$. If they have (collectively) special scale-invariant correlations, the entropy $S_q\equiv k\,[1- \sum_i p_i^q]/(q-1)$ (with $S_1=S_{BG}$) satisfies, for some value of $q\ne1$, $S_q(N)=NS_q(1)$, and is therefore additive, hence {\it extensive}. We exhibit two paradigmatic systems (one discrete and one continuous) for which the entropy $S_q$ is additive, whereas $S_{BG}$ is neither strictly nor asymptotically so. We conjecture that this mechanism is deeply related to the nearly ubiquitous emergence, in natural and artificial complex systems, of scale-free structures.
- Año
- 2005
- Número
- CBPF-NF-006/05
- Vínculo con tesis
- No
- Vínculo con beca
- No