A pathway to multivariate Gaussian density

TL;DR

This paper introduces a principle called 'conservation of the ellipsoid of concentration' and derives a generalized entropic pathway that leads to the multivariate Gaussian density, unifying several entropic forms.

Contribution

It proposes a new principle and a generalized entropic pathway that connects various entropic forms to the multivariate Gaussian density.

Findings

Derives a pathway to multivariate Gaussian density

Unifies Boltzmann-Gibbs and Tsallis entropic forms

Provides a new framework for density optimization

Abstract

A general principle called "conservation of the ellipsoid of concentration" is introduced and a generalized entropic form of order 'alpha' is optimized under this principle. It is shown that this can produce a density which can act as a pathway to multivariate Gaussian density. The resulting entropic pathway contains as special cases the Boltzmann-Gibbs (Shannon) and Tsallis (Havrda-Charvat) entropic forms.