The entropic character of the atomic level stress in polymeric melts and the stress optical coefficient are studied in model systems by the use of equilibrium and nonequilibrium molecular dynamics. The atomic level stress is defined in intrinsic coordinates, a mobile frame tied to the generic bond. The global stress sigma is obtained in the global coordinate system by summing up the contributions due to the intrinsic stress corresponding to each atom in the population. The atom-based global stress is proportional to an average measure of bond orientation (P-2), With the proportionality constant sigma /P-2 being related td the macroscopic stress optical coefficient (SOC). The proportionality constant may be expressed in terms of intrinsic quantities which, in turn, are computable from equilibrium simulations. The model reproduces most, experimentally observed properties of the SOC. The ratio sigma /P-2 is chain length and deformation rate independent in the melt and becomes rate dependent in the glassy state. The dependence of the global stress on temperature at imposed average bond orientation is therefore determined by the variation of the intrinsic stresses with temperature. The stress is purely entropic in the melt for all chain lengths. However, neither one of its components, that due to bonded and that due to nonbonded interactions, is purely entropic. The global stress a acquires an energetic component at high temperatures and at large deformations, when chains are significantly stretched. The entropic character of the atomic level stress is shown to be due to packing effects, similar to the situation encountered in simple fluids. These conclusions remain unchanged upon variation of the model parameters such as the stiffness of the nonbonded and bonded interatomic potential, the cutoff radius of the nonbonded potential, and the bond length.