And yet it moves - or does it? Spurious drifts at equilibrium

When diffusion depends on the state of a system, the drift measured from its trajectories contains a spurious part unrelated to forces. At equilibrium, particles can then appear to sediment, repel each other, even rotate - the same way whether the movie is played forward or backward. Drifts are conditional averages, not currents: they carry meaning only together with a consistently inferred diffusion tensor. Paired with the wrong one, they make passive particles look active. I show how to infer spurious drifts from trajectory moments alone, enabling thermodynamically consistent inference.