  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.
