International Journal of Catalysis and Chemical Engineering
Analytical Information Links Between Fisher's Measure and Gibbs' Ensembles
Abstract
F. Pennini and A. Plastino
This is a purely analytical information theory work. We will uncover interesting links between Fisher’s mea- sure and Gibbs’ ensembles, particulary the grand canonical and canonical ones, each offering distinct insights into a system’s properties. In this effort, we construct an informational connection between these ensembles, based on Fisher’s measure.
We specifically explore the relationships among four key concepts:
• The canonical and grand canonical ensembles.
• Fisher information measures applied to three parameters (inverse tempera- ture, particle number, and fugacity).
• The Fano factor.
• Special Poisson probability distributions (PDs) that are related to grand canonical PDs by having the same mean particle number ⟨N⟩.
Our findings reveal intri- cate and compelling relationships among these concepts, providing new perspectives on the interplay between statistical mechanics and information theory.