Experimental determination of the non-extensive entropic parameter $q$

TL;DR

This paper demonstrates how to determine the non-extensive entropic parameter q from experimental data in inhomogeneous magnetic systems, linking microscopic cluster distributions to macroscopic properties.

Contribution

It introduces a method to extract the q parameter from experimental data and relates it to the system's dynamics and non-extensive thermodynamics.

Findings

Measured q parameter in La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ using tunnelling spectroscopy.

Predicted bulk magnetization with good accuracy based on q.

Connected non-extensivity to the Griffiths phase in magnetic systems.

Abstract

We show how to extract the $q$ parameter from experimental data, considering an inhomogeneous magnetic system composed by many Maxwell-Boltzmann homogeneous parts, which after integration over the whole system recover the Tsallis non-extensivity. Analyzing the cluster distribution of La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ manganite, obtained through scanning tunnelling spectroscopy, we measure the $q$ parameter and predict the bulk magnetization with good accuracy. The connection between the Griffiths phase and non-extensivity is also considered. We conclude that the entropic parameter embodies information about the dynamics, the key role to describe complex systems.