Stress production in a model monodisperse polymeric material is investigated on multiple scales. The analysis is performed by means of equilibrium and nonequilibrium molecular dynamics. A family of mobile intrinsic coordinate systems is introduced, each system having one axis tied to the end-to-end vector of a generic chain segment of specified length. A similar mobile coordinate system tied to the large semiaxis of the ellipsoidal chains is defined on the chain scale. The atomic level stress is evaluated based on bonded and nonbonded interatomic interactions and averaged in the global coordinate system, to result in the global, system level stress, and in the various intrinsic systems, to result in intrinsic stresses. It is observed that the deviatoric intrinsic stress is scale independent, a bond, a chain segment, and the chain scale intrinsic frame carrying the same stress. The hydrostatic component of the stress tensor scales with the segment length. This concept extends the previously introduced intrinsic stress framework, scale linking the bond and chain scales. During melt deformation, the chain segments stretch and rotate. Chains shorter than the entanglement length mainly rotate during an elongational deformation of limited amplitude, their size remaining essentially constant. Longer chains distort and rotate. Two regimes are evidenced during the return to isotropy of the orientation on multiple scales. The faster mode is associated with the return to equilibrium of the internal structure of the generic chain, while the slower mode is associated with chain rotation in the global coordinate system. The intrinsic deviatoric stress carried by a chain changes during the first mode, and is essentially constant during the second. The physical picture of stress production defined on the scale of a bond (Kuhn segment) in the intrinsic stress framework translates to the chain scale during this late relaxation regime: each rotating chain carries a constant deviatoric intrinsic stress, the preferential chain orientation leading to a nonzero global deviatoric stress.