Reciprocity relations and generalized entropic quantifiers that lack trace-form

TL;DR

This paper demonstrates that Legendre reciprocity relations are upheld by all entropic functionals regardless of trace-form, and discusses how to resolve anomalies in reciprocity relations in certain variational cases.

Contribution

It reveals that reciprocity relations are valid for any entropic functional, not just trace-form, and provides methods to address anomalies in physical applications.

Findings

Reciprocity relations hold for all entropic functionals.

Anomalies in reciprocity relations can be corrected by distinguishing entropic forms.

The study applies to physical systems using maximum entropy principles.

Abstract

In this effort we show that the Legendre reciprocity relations,thermodynamic's essential formal feature, are respected by any entropic functional, even if it is NOT of trace-form nature, as Shannon's is. Further, with reference to the MaXent variational process, we encounter important cases, relevant to physical applications currently discussed in the research literature, in which the associated reciprocity relations exhibit anomalies. We show that these anomalies can be cured by carefully discriminating between apparently equivalent entropic forms.