Sufficiency of equilibrium-profile asymmetry for rectification

Determine whether broken spatial-reflection symmetry of the equilibrium density profile is sufficient to guarantee rectification-like behavior in a fixed realization of the boundary-driven symmetric exclusion process with quenched site disorder.

Background

The paper proves that spatial-reflection symmetry of the equilibrium density profile guarantees antisymmetry of the current under reversal of the reservoir density difference. Consequently, broken reflection symmetry is a necessary condition for sample-specific rectification-like behavior. However, nonlinear current contributions may cancel even when the equilibrium profile is asymmetric, so the paper does not establish whether the necessary condition is also sufficient.

References

The exact symmetry argument does not establish whether this condition is sufficient. In principle, cancellations among nonlinear current contributions could restore current antisymmetry. Thus, an asymmetric equilibrium density profile permits but does not guarantee rectification-like behavior.

— Sample-specific rectification-like response in a boundary-driven exclusion process  (2609.03560 - Sakai et al., 3 Sep 2026) in Section 5, Discussion

The present results, however, do not determine the asymptotic scaling with $L$ or establish whether the rectification measure vanishes in the thermodynamic limit.

— Sample-specific rectification-like response in a boundary-driven exclusion process  (2609.03560 - Sakai et al., 3 Sep 2026) in Appendix, Section “Dependence on the reservoir parameters”; see also Section 5, “Distribution and finite-size behavior of rectification”