Isothermal-isobaric molecular dynamics simulations are used to calculate the specific volume of models of trehalose and three amorphous trehalose-water mixtures (2.9%, 4.5% and 5.3% (w/w) water, respectively) as a function of temperature. Plots of specific volume versus temperature exhibit a characteristic change in slope when the amorphous systems change from the glassy to the rubbery state and the intersection of the two regression lines provides an estimate of the glass transition temperature T(g). A comparison of the calculated and experimental T(g) values, as obtained from differential scanning calorimetry, shows that despite the predicted values being systematically higher (about 21-26K), the trend and the incremental differences between the T(g) values have been computed correctly: T(g)(5.3%(w/w))<T(g)(4.5%(w/w))<T(g)(2.9%(w/w))<T(g)(0.0%(w/w)). The mobility of water has been investigated over temperature ranges covering the rubbery and the glassy phases of the trehalose-water mixtures by calculating the diffusion coefficients of water. The temperature dependence of the diffusion coefficient changes in the region of the glass transition and can be used as well to estimate T(g) values. The activation energies for water diffusion were found to be independent of the amount of water in amorphous trehalose.