We perform molecular dynamics simulations of the glass transition through isobaric and isochoric cooling of a model polymeric material. In general, excellent agreement between the simulation results and the existing experimental trends is observed. The glass transition temperature (T (g)) is found to be a function of pressure under isobaric conditions and specific volume under isochoric conditions. Under both isobaric and isochoric conditions, the trans-state fraction and the torsional contributions to the energy undergo abrupt changes at the glass transition temperature. We analyze these data to show that the glass transition is primarily associated with the freezing of the torsional degrees of the polymer chains which is strongly coupled to the degree of freedom associated with the nonbonded Lennard-Jones potential. We attribute the greater strength of the glass transition under constant pressure conditions to the fact that the nonbonded Lennard-Jones potential is sensitive to the specific volume, which does not change during cooling under isochoric conditions. Comparison of the isochoric and isobaric data demonstrate that the thermodynamic state is independent of cooling path above T (g), while path-dependent below T (g). The simulation data show that the free volume at the isobaric glass transition temperature is pressure dependent. We also find that a glass transition occurs under isochoric conditions, even though the free volume actually increases with decreasing temperature.