Sample-specific rectification-like response in a boundary-driven exclusion process

What the math gives to ML

The paper identifies a concrete transport mechanism: quenched, sample-specific spatial heterogeneity produces an even-in-drive current component, J(delta) = a1 delta + a2 delta^2 + ..., even though the disorder ensemble remains symmetric. The decisive condition is broken spatial-reflection symmetry of the realized equilibrium profile; reflection-symmetric samples have a2 = 0. A transferable neural analogue is a recurrent or state-space module with fixed heterogeneous local time scales, whose response to opposite signed inputs can be deliberately rectified. The paper therefore suggests a testable architecture for directional sequence processing, with a sharp symmetry prediction rather than only a benchmark hypothesis.