Revisiting the Ratchet Principle: When Hidden Symmetries Prevent Steady Currents

TL;DR

This paper investigates exceptions to the ratchet principle in active and passive systems, revealing hidden symmetries and conservation laws that can prevent steady currents despite parity violation.

Contribution

It identifies hidden time-reversal symmetry and momentum conservation as key factors that can inhibit ratchet currents, refining the understanding of conditions for non-equilibrium steady states.

Findings

Hidden time-reversal symmetry prevents ratchet currents at low densities.

Emergent momentum conservation can inhibit currents at higher densities.

The presence of conservation laws modifies the traditional ratchet principle.

Abstract

The "ratchet principle", which states that non-equilibrium systems violating parity symmetry generically exhibit steady-state currents, is one of the few generic results outside thermal equilibrium. We study exceptions to this principle observed in active and passive systems with spatially varying fluctuations sources. For dilute systems, we show that a hidden time-reversal symmetry prevents the emergence of ratchet currents. At higher densities, pairwise forces break this symmetry but an emergent conservation law for the momentum field may nevertheless prevent steady currents. We show how the presence of this conservation law can be tested analytically and characterize the onset of ratchet currents in its absence. Our results show that the ratchet principle should be amended to preclude parity symmetry, time-reversal symmetry, and bulk momentum conservation.