Thermostat-induced artificial lane formation in non-equilibrium molecular dynamics

While most thermostats in molecular dynamics are designed for equilibrium systems, their extension to non-equilibrium simulations has little theoretical justification. In the literature, an artifact referred to as "lane formation" was discovered; however, its cause remained unclear and was simply attributed to a constraint on velocity fluctuations or non-ergodicity in thermostats. In addition, global deterministic thermostatted dynamics was found to exhibit unceasing phase-space compression in steady states, incompatible with their expected stationary distributions and Gibbs entropy, which was mistakenly perceived as inescapable. In this work, we pinpoint that the dynamical cause of artificial lane formation is a stable fixed point in the momentum space induced by improper velocity rescaling, which produces effective repulsion between different species in a color flow, drains transverse kinetic energy and generates the unceasing compression. This artifact is deeply rooted in global deterministic thermostats, such as the Nosé-Hoover dynamics and configurational thermostat. With proper rescaling, the Langevin thermostat completely eliminates artificial lane formation and exemplifies how incompressible phase space and stationary distributions can be retained for non-equilibrium steady states.