Scale invariance and related properties of \(q\)-Gaussian systems. (English) Zbl 1203.82005
Summary: We advance scale-invariance arguments for systems that are governed (or approximated) by a \(q\)-Gaussian distribution, i.e., a power law distribution with exponent \(Q=1/(1 - q); Q\in \mathbb R\). The ensuing line of reasoning is then compared with that applying for Gaussian distributions, with emphasis on dimensional considerations. In particular, a Gaussian system may be part of a larger system that is not Gaussian, but, if the larger system is spherically invariant, then it is necessarily Gaussian again. We show that this result extends to \(q\)-Gaussian systems via elliptic invariance. The problem of estimating the appropriate value for the Tsallis’ parameter \(q\) is revisited. A kinetic application is also provided.
MSC:
| 82B03 | Foundations of equilibrium statistical mechanics |
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