The dependence of information entropy of uniform Fermi systems on correlations and thermal effects

TL;DR

This paper investigates how correlations and thermal effects influence the Shannon information entropy in uniform Fermi systems like nuclear matter, electron gas, and liquid helium-3, revealing that both factors similarly affect entropy through kinetic energy.

Contribution

It introduces a two-parameter model linking the correlated part of entropy to the correlation parameter and kinetic energy, and explores thermal effects on entropy in electron gases.

Findings

Correlation parameters characterize the strength of correlations.

The thermal and correlation effects on entropy are quantitatively similar.

Entropy values are nearly the same regardless of whether changes are due to correlations or temperature.

Abstract

The influence of correlations of uniform Fermi systems (nuclear matter, electron gas and liquid $^3$He) on Shannon's information entropy, $S$, is studied. $S$ is the sum of the information entropies in position and momentum spaces. It is found that, for three different Fermi systems with different particle interactions, the correlated part of $S$ ($S_{cor}$) depends on the correlation parameter of the systems or on the discontinuity gap of the momentum distribution through two parameter expressions. The values of the parameters characterize the strength of the correlations. A two parameter expression also holds between $S_{cor}$ and the mean kinetic energy ($K$) of the Fermi system. The study of thermal effects on the uncorrelated electron gas leads to a relation between the thermal part of $S$ ($S_{thermal}$) and the fundamental quantities of temperature, thermodynamical entropy and the mean kinetic energy. It is found that, in the case of low temperature limit, the expression connecting $S_{thermal}$ with $K$ is the same to the one which connects $S_{cor}$ with $K$. There are only some small differences on the values of the parameters. Thus, regardless of the reason (correlations or thermal) that changes $K$, $S$ takes almost the same value.