Power-Law distributions and Fisher's information measure

TL;DR

This paper explores how thermodynamic uncertainties maintain their form when transitioning from Boltzmann-Gibbs to Tsallis statistics, emphasizing the importance of conjugate variables in nonextensive thermodynamics.

Contribution

It demonstrates the invariance of thermodynamic uncertainties under the shift from classical to nonextensive statistical frameworks using Fisher's information measure.

Findings

Thermodynamic uncertainties preserve their form in Tsallis' statistics.

Proper conjugate variables are essential in nonextensive thermodynamics.

Fisher's information measure is key to understanding these invariances.

Abstract

We show that thermodynamic uncertainties (TU) it preserve their form in passing from Boltzmann-Gibbs' statistics to Tsallis' one provided that we express these TU in terms of the appropriate variable conjugate to the temperature in a nonextensive context.