Computer simulations of liquid and solid systems very close to the mel
ting-freezing transition zone have been performed for the microcanonic
al, canonical, and isothermal-isobaric molecular-dynamics ensembles. T
emperature, pressure, and density fluctuations were studied over long
evolution times, and graphical and analytical statistical-error method
s were used to investigate correlations in the data. The Nose-Hoover (
NH) method combined with the Toxvaerd algorithm is proposed as a corre
ct method of obtaining the true fluctuation and correlation of the the
rmodynamic variables in the system, because the temperature and/or pre
ssure constraints in the NH method do not affect the dynamical evoluti
on of the system, and because the fifth-order Toxvaerd algorithm gives
very accurate behavior for the correlations, as has been shown in rec
ent studies.