  Using a non-perturbative classical model, we numerically investigate the
dynamics of mobile particles interacting with an infinite chain of harmonic
oscillators, an abstraction of ionic conduction through solid-state materials.
We show that coupling between the mobile particles and a single mass of the
chain is sufficient to induce dissipation of the mobile particles' energy over
a wide range of system parameters. When we introduce thermal fluctuations in
the position of the chain mass, the mobile particles exhibit thermalization,
eventually reaching the same temperature scale as the chain. This model
demonstrates how a minimal set of ingredients can exhibit a link between
microscopic motion and macroscopic observables, with computationally efficient
simulations. Finally, we suggest some experimental platforms that could realize
such a model.
