English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We analyze the distribution that extremizes a linear combination of theBoltzmann--Gibbs entropy and the nonadditive $q$-entropy. We show that thisdistribution can be expressed in terms of a Lambert function. Both the entropicfunctional and the extremizing distribution can be associated with a nonlinearFokker--Planck equation obtained from a master equation with nonlineartransition rates. Also, we evaluate the entropy extremized by a linearcombination of a Gaussian distribution (which extremizes the Boltzmann--Gibbsentropy) and a $q$-Gaussian distribution (which extremizes the $q$-entropy). Wegive its explicit expression for $q=0$, and discuss the other casesnumerically. The entropy that we obtain can be expressed, for $q=0$, in termsof Lambert functions, and exhibits a discontinuity in the second derivative forall values of $q<1$. The entire discussion is closely related to recent resultsfor type-II superconductors and for the statistics of the standard map.

On the connection between linear combination of entropies and linear combination of extremizing distributions