Majorization properties of generalized thermal distributions

TL;DR

This paper investigates the majorization properties of generalized thermal distributions, identifying conditions for increased mixedness and analyzing distributions with power law behavior characterized by temperature and non-extensivity parameters.

Contribution

It provides new sufficient conditions for mixedness increase in thermal-like states and characterizes power law distributions with two key parameters.

Findings

Conditions for increased mixedness are established.

Power law distributions are characterized by temperature and q.

Numerical results illustrate theoretical findings.

Abstract

We examine the majorization properties of general thermal-like mixed states depending on a set of parameters. Sufficient conditions which ensure the increase in mixedness, and hence of any associated entropic form, when these parameters are varied, are identified. We then discuss those exhibiting a power law distribution, showing that they can be characterized by two distinct mixing parameters, one associated with temperature and the other with the non-extensivity index q. Illustrative numerical results are also provided.