“…Non-or weakly dissipative models have been used to explain phenomena such as dislocation motion [1], ferromagnetic domain wall motion [2], proton mobility in hydrogen-bonded chains [3], rotation of DNA bases [4], chains of rotating pendula [5], or lattices of bistable buckled, elastic structures [6]. By contrast, diffusive or dissipative kinetics play an essential role in describing the physics of, e.g., ferroelectric domain switching [7], dynamics of CNT foams [8,9], magnetic flux propagation in Josephson junctions with tunneling losses [10], pulse propagation in cardiophysiology [11] and neurophysiology [12], sliding friction [13], chemical surface adsorption [14], underdamped commensurate phase transitions [15], or defect conductivity in superionic conductors [16]. Although numerous theoretical studies have been devoted to characterizing the motion of phase boundaries particularly in 1D periodic physical, chemical, or biological systems, see, e.g.…”