Structurally controlled Frenkel relaxation time in liquids

We present a physically consistent framework for describing momentum transport in liquids in which the Frenkel relaxation time is determined by structural rearrangements encoded in a free-energy landscape. Collective shear-carrying rearrangements are represented by a structural deformation variable. Self-consistent statistical averaging gives a nonlinear relation between the effective field and the structural strain, identifies monostable and bistable regimes, and defines the activation barrier between competing structural states. This barrier determines a state-dependent Frenkel relaxation time in activated form. The resulting relaxation time is introduced into a Maxwell-type hydrodynamic description, which connects structural kinetics with viscosity, the Deborah number, and the emergence of a gapped momentum state. The formulation is evaluated using rheological data for a non-Newtonian liquid through the experimentally reconstructed relaxation parameter. Because the structural parameter is reconstructed from the same dataset, the comparison is treated as a calibrated consistency test rather than an independent prediction. The results show that the reconstructed Frenkel time can serve as a physically interpretable descriptor of the shear-rate-dependent transport regime and provides a consistent representation of the measured viscosity response.