Stokes-Type Entropic Force Driving Nanoscale Phonon-Mediated Superlubricity in 2D Materials

This Communication addresses a superlubric state in graphene-type layers in nanoscale conditions. We focus on the superlubric state based on the twofold generation and propagation of (thermal) phonons. In the first instance, phonon propagation has a local mode in the graphene-type lattice, whereas in the second instance, it can spread globally. In the former, we see that the kinematic harmonic-mean-type speed condition underlies the mechanism of phonon propagation. In the latter, an arithmetic-mean fingerprint, pointing to a constant acceleration case, can be applied. We disclose a linear phonon-propagation mechanism with an entropic force behind it. Under a passage between classical and quantum domains, this entropic force is equivalent to a Stokes-type force (linear in the sliding speed) with a resultant involvement of a quantum fluctuation-dissipation relation, including a "double quantum" of thermal energy and the apparent (quantum viz. nanoscale) viscosity. The corresponding entropy-production conditions are derived and critically discussed within this framework, establishing a direct thermodynamic link between microscopic (physical) information-processing events and mesoscopic phonon transport. The resulting unified classical-quantum description of entropy-driven phonon-mediated superlubricity constitutes the principal novelty of the present work and may be relevant for future developments in nanotechnology and advanced materials engineering.