Maximum entropy with fluctuating constraints: The example of K-distributions

Abstract : We indicate that in a maximum entropy setting, the thermodynamic β and the observation constraint are linked, so that fluctuations of the latter imposes fluctuations of the former. This gives an alternate viewpoint to ‘superstatistics’. While a Gamma model for fluctuations of the β parameter gives the so-called Tsallis distributions, we work out the case of a Gamma model for fluctuations of the observable, and show that this leads to K-distributions. We draw attention to the fact that these heavy-tailed distributions have high interest in physical applications, and we discuss them in some details.
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Jean-François Bercher. Maximum entropy with fluctuating constraints: The example of K-distributions. Physics Letters A, Elsevier, 2008, 372 (24), pp.4361-4363. ⟨10.1016/j.physleta.2008.04.016⟩. ⟨hal-00621950⟩

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