  A novel method to determine the density and temperature of a system is
proposed based on quantum fluctuations typical of Fermions in the limit where
the reached temperature T is small compared to the Fermi energy $\epsilon_f$ at
a given density $\rho$. Quadrupole and particle multiplicity fluctuations
relations are derived in terms of $\frac{T}{\epsilon_f}$. This method is valid
for infinite and finite fermionic systems, in particular we apply it to heavy
ion collisions using the Constrained Molecular Dynamics (CoMD) approach which
includes the Fermi statistics. A preliminary comparison to available
experimental data is discussed as well. We stress the differences with methods
based on classical approximations. The derived 'quantum' temperatures are
systematically lower than the corresponding 'classical' ones. With the proposed
method we may get important informations on the Equation of State (EOS) of
quantum Fermi systems to order O($\frac{T}{\epsilon_f})^3$, in particular near
the Liquid-Gas (LG) phase transition and at very low densities where quantum
effects are dominant.
