A Markovian approach to the Prandtl-Tomlinson frictional model

Abstract

We consider the Prandtl-Tomlinson model in the case of a constant driving force and in the presence of thermal fluctuations. We show that the system dynamics is well reproduced by a simplified description obtained through a Markov process, even in the case of potentials with several minima. After estimating the chain parameters by numerical simulation, we compute the average velocity and friction at varying driving force and temperature. Then we take advantage of this approach for calculating the entropy produced by the system and, in the case of a single minimum potential, to derive its explicit relation with the external force and the mobility at low temperatures. We observe that the coefficient relating the entropy production to the force is not a monotonic function of the temperature.

arXiv comment15 pages, 12 figures

References in corpus (6)

• Modeling friction: From nanoscale to mesoscale
• The Fluctuation Theorem as a Gibbs Property
• Velocity dependence of atomic-scale friction: a comparative study of the one- and two-dimensional Tomlinson model
• Quantum oscillations near the metamagnetic transition in Sr3Ru2O7
• Master equation approach to friction at the mesoscale
• Thermodynamic aspects of nanoscale friction