Three-body problem for Langevin dynamics with different temperatures
Abstract
A mixture of Brownian particles at different temperatures has been a useful model for studying the out-of-equilibrium properties of systems made up of microscopic components with differing levels of activity. This model was previously studied analytically for two-particle interactions in the dilute limit, yielding a Boltzmann-like two-particle distribution with an effective temperature. Like the Newtonian two and three-body problems, we ask here whether the two-particle results can be extended to three-particle interactions to get the three-particle distributions. By considering the special solvable case of pairwise quadratic interactions, we show that, unlike the two-particle distribution, the three-particle distribution cannot in general be Boltzmann-like with an effective temperature. We instead find that the steady state distribution of any two particles in a triplet depends on the properties of and interactions with the third particle, leading to some unexpected behaviors not present in equilibrium.
Cite
@article{arxiv.1911.11127,
title = {Three-body problem for Langevin dynamics with different temperatures},
author = {Michael Wang and Alexander Grosberg},
journal= {arXiv preprint arXiv:1911.11127},
year = {2020}
}