Generalization of Completely Monotone Conjecture for Tsallis entropy

TL;DR

This paper extends the completely monotone conjecture from Shannon entropy to Tsallis entropy for orders up to four, using an algorithm based on systematic integrations-by-parts.

Contribution

It generalizes the conjecture to Tsallis entropy and applies a systematic integration-by-parts algorithm for proof.

Findings

Conjecture holds for Tsallis entropy up to order four

Algorithm successfully verifies monotonicity properties

Extension from Shannon to Tsallis entropy achieved

Abstract

We generalize the completely monotone conjecture ([CG15]) from Shannon entropy to the Tsallis entropy up for orders up to at least four. To this end, we employ the algorithm ([J\"un16, JM06a]) which employs the technique of systematic integrations-by-parts.