Heavy ion collisions can be used to study the thermodynamics of hot an
d dense nuclear matter only if the initial mass and energy fluctuation
s that lead to fragmentation are of thermal origin and survive the dis
assembly process. If this is the case, the observed fragment multiplic
ity should be directly related to those initial fluctuations and to th
e conditions of temperature and density causing them. The feasibility
of this scenario is demonstrated with a molecular dynamics study of th
e evolution of mass and energy fluctuations, and fluctuations of the p
hase-space density. First, it is verified that the fluctuations leadin
g to fragmentation are indeed early ones; Second, it is determined tha
t different initial conditions of density and temperature can indeed p
roduce varying final fragment multiplicities. The rho-T plane is mappe
d to the fragment multiplicity with good precision. This mapping shoul
d be easily reproducible with existing experimental data.