Determine whether terminal-width statistics contain independent spectral information

Determine whether the statistical terminal width of the polymer relaxation spectrum represents information beyond that contained in the ensemble-averaged stress-weighted eigenvalue spectrum.

Background

The molecular derivation produces the two algebraic branches of the BSW spectrum and identifies a finite terminal cutoff associated with tube renewal or disengagement. However, it does not determine the detailed statistical shape or width of that terminal edge. The unresolved issue is whether a statistically broadened terminal crossover reflects genuinely additional information about terminal molecular relaxation, or whether it is already encoded in the ensemble-averaged spectrum of stress-weighted relaxation eigenvalues.

References

Whether the statistical terminal width represents information beyond that already contained in the ensemble-averaged stress-weighted eigenvalue spectrum remains an open question of the present molecular theory.

— Microscopic origin of the Baumgärtel-Schausberger-Winter Relaxation Spectrum in Polymer Melts and Particle Rafts  (2609.29720 - Nichetti et al., 24 Sep 2026) in Section “Emergent relaxation spectrum,” immediately after Eq. (w), terminal-relaxation discussion