Activity Without Activity: Boundary-Induced Drift and Negative Mobility in Passive Dimers

We identify a general mechanism by which Skorohod reflections at hard boundaries generate steady probability fluxes and directed motion in purely passive diffusive systems. This boundary-induced asymmetry acts as an autonomous motor, rectifying thermal fluctuations without self-propulsion or energy injection. We illustrate the mechanism in a minimal one-dimensional dimer of two overdamped Brownian particles with hard-core exclusion and unequal diffusivities. Mapping to a two-dimensional Fokker–Planck equation shows that the reflection term along the confinement boundary creates a net flux parallel to the boundary. Crucially, unequal diffusivities break exchange symmetry and select the drift direction toward the higher-diffusivity ("hotter") particle. When a uniform bias is applied, the same boundary mechanism produces absolute negative mobility, with a sharp transition between positive and negative response delineated in the diffusivity–force plane. Our results establish Skorohod reflection as a minimal route to autonomous motor behavior and symmetry-broken transport in passive mixtures.