Higher Order Corrections to Density and Temperature of Fermions from Quantum Fluctuations

TL;DR

This paper extends a method based on quantum fermionic fluctuations to high-temperature regimes, deriving relations for fluctuations, providing analytical formulas, and comparing quantum and classical entropies near phase transitions.

Contribution

It generalizes fluctuation-based density and temperature determination methods to high temperatures, offering analytical formulas and insights into entropy behavior near phase transitions.

Findings

Derived relations for quadrupole and particle multiplicity fluctuations at high T

Provided analytical formulas matching numerical solutions for all T

Showed good agreement between quantum and classical entropy estimates at low densities

Abstract

A novel method to determine the density and temperature of a system based on quantum Fermionic fluctuations is generalized to the limit where the reached temperature T is large compared to the Fermi energy {\epsilon}f . Quadrupole and particle multiplicity fluctuations relations are derived in terms of T . The relevant Fermi integrals are numerically solved for any values of T and compared to the analytical approximations. The classical limit is obtained, as expected, in the limit of large temperatures and small densities. We propose simple analytical formulas which reproduce the numerical results, valid for all values of T . The entropy can also be easily derived from quantum fluctuations and give important insight for the behavior of the system near a phase transition. A comparison of the quantum entropy to the entropy derived from the ratio of the number of deuterons to neutrons gives a very good agreement especially when the density of the system is very low.