On the way towards a generalized entropy maximization procedure

TL;DR

This paper introduces a generalized entropy maximization method that incorporates generalized averaging and information gain, leading to new stationary distributions for Renyi and Tsallis entropies.

Contribution

It presents a novel generalized entropy maximization framework applicable to Renyi and Tsallis entropies, unifying and extending previous approaches.

Findings

Exponential stationary distributions for Renyi entropy with q in [0,1].

All stationary distributions for Tsallis entropy can be derived using generalized transforms.

The method bridges different entropy-based stationary distributions.

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.