We apply the cooperative free volume (CFV) model to analyze the segmental relaxation times, r(T,V), of a model 20-mer polymer melt simulated via molecular dynamics over a broad pressure range. Thermodynamic characterization of the 20-mer allows determination of the constant contribution from the hard-core volume (V-hc), which then yields predictions for the free volume, V-free = V - V-hc. The CFV rate model is based on an activation free energy that increases with the number of cooperating segments, n*, wherein the system's free volume, V-free, is what determines n*. The model predicts that on isotherms ln tau vs 1/V(free)( )is linear with T-dependent slopes. The 20-mer melt data follow this linear behavior at all temperatures. Assuming a fixed activation energy per cooperating segment leads to a very simple analytic form that describes all of the 20-mer melt's high T behavior, including the Arrhenius to non-Arrhenius transition regime. This form reflects the importance of a gas kinetic contribution as well as both energetic and entropic contributions to the activation energy. Optimization of only one material-dependent parameter leads to collapse of the data. The results of this paper reveal that a key source of non-Arrhenius behavior with decreasing T along isobars is the reduction in V(free )which means that segmental rearrangement will require increased cooperativity and higher activation energy. This effect explains the volume contribution to dynamics.