Scale invariance and related properties of q-Gaussian systems

C.VIGNAT; A.PLASTINO

PHYSICS LETTERS A

Año: 2007 p. 370 - 375

0375-9601

Abstract 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 ∈ 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.q-Gaussian distribution, i.e., a power law distribution with exponent Q = 1/(1 − q); q ∈ 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.Q = 1/(1 − q); q ∈ 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.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.q is revisited. A kinetic application is also provided. © 2007 Elsevier B.V. All rights reserved.2007 Elsevier B.V. All rights reserved.