Energy Exchange Calculations in a Simple Mechanical System to Investigate the Origin of Friction

TL;DR

This study uses a simple classical 1D two-particle system to explore the microscopic origins of friction, revealing complex energy exchange behaviors that mimic dissipative forces without explicit damping terms.

Contribution

It introduces a minimalistic model to analyze how energy transfer between particles can produce emergent friction-like dissipation.

Findings

Energy exchange depends on system parameters.

Emergent dissipation arises from classical interactions.

Qualitative agreement with friction phenomenology.

Abstract

The microscopic origin of friction is an important topic in science and technology. To date, noteworthy aspects of it remain unsolved. In an effort to shed some light on the possible mechanisms that could give rise to the macroscopic emergence of friction, a simple 1Dd system of two particles is considered, one of them free but moving with an initial velocity, and the other confined by a harmonic potential. The two particles interact via a repulsive Gaussian potential. While it represents in a straightforward manner a tip substrate system in the real world, no analytical solutions can be found for its motion. Because of the interaction, the free particle (tip) may overcome the bound particle (substrate) losing part of its kinetic energy. We solve the Newton's equations of the two particles numerically and calculate the net exchange of energy in the asymptotic state in terms of the relevant parameters of the problem. The effective dissipation that emerges from this simple, classical model with no ad hoc terms shows, surprisingly, a range of rich, non-trivial, behavior. We give theoretical reasoning which provides a satisfactory qualitative description. The essential ingredient of that reasoning is that the transfer of energy from the incoming particle to the confined one can be regarded as the source of the emergent dissipation force, the friction experienced by the incoming particle.