On the way towards a generalized entropy maximization procedure

Abstract

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Renyi and Tsallis entropies. The generalized entropy maximization procedure for Renyi entropies results in the exponential stationary distribution asymptotically for q is between [0,1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure.

12 pages, no figures

References in corpus (3)

• Escort mean values and the characterization of power-law-decaying probability densities
• Controlled decoherence in a quantum Lévy kicked rotator
• Generalized entropic structures and non-generality of Jaynes' Formalism

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• The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies
• Non-Extensive Transport Equations in Magnetized Plasmas