Golden-Thompson's inequality for deformed exponentials
Frank Hansen
TL;DR
This paper extends the Golden-Thompson inequality to q-exponentials within the range [1,3], which are key in non-extensive statistical mechanics and entropy theories.
Contribution
It formulates and proves a new version of the Golden-Thompson inequality for deformed exponentials with parameter q in [1,3].
Findings
Established a Golden-Thompson inequality for q-exponentials.
Extended the inequality to a new range of q in [1,3].
Contributed to the mathematical foundation of non-extensive entropy theories.
Abstract
Deformed logarithms and their inverse functions, the deformed exponentials, are important tools in the theory of non-additive entropies and non-extensive statistical mechanics. We formulate and prove counterparts of Golden-Thompson's trace inequality for q-exponentials with parameter q in the interval [1,3].
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