Parity Selection Rule for Information and Dissipation in Driven Steady States

2026-06-17

AI Summary

This study investigates whether a tight equality relation exists between symmetry-resolved information and entropy production in rotationally driven linear nonequilibrium steady states. Combining stochastic thermodynamics, matrix analysis, and rotational symmetry theory—augmented by heavy-tailed Lévy noise modeling—the work establishes a parity selection rule governed by the commutativity of relaxation and diffusion matrices. Under specific symmetry conditions, the mutual information becomes an even function of the driving parameter, while entropy production scales quadratically with the drive strength; closed-form expressions for both quantities are derived. Theoretical predictions yield a planar mutual information of approximately 0.145 nats and an explicit prefactor for entropy production, alongside the existence of only a one-sided thermodynamic uncertainty bound. These results are validated through circuit-level simulations of a Brownian gyroscope and accompanied by a falsifiable experimental proposal.

Abstract

Tight equalities between symmetric information and entropy production in driven steady states remain elusive. We show that they are forbidden by a parity selection rule for rotation-driven linear nonequilibrium steady states. Whenever the relaxation and diffusion matrices commute, the snapshot mutual information between two time slices is exactly even under drive reversal, and parity violation rises linearly in the commutator norm when alignment is broken. Full isotropy strengthens this to drive-independence, and the planar mutual information takes the closed-form value of about 0.145 nats. Under the same alignment, the entropy production is exactly quadratic in the drive, and its prefactor admits an explicit closed form in the traces and determinant of the two matrices. The orthogonality of even and odd sectors leaves only one-sided thermodynamic-uncertainty bounds. The rule rests on the rotational symmetry of the drift alone and survives heavy-tailed isotropic stable noise with tail index below two, where variance-based bounds become vacuous. A falsifiable test is proposed on an electrical Brownian gyrator augmented for independent drive control with circuit-level stable-noise injection.

Problem

• parity selection rule
• driven steady states
• mutual information
• entropy production
• nonequilibrium thermodynamics

Innovation

• parity selection rule
• nonequilibrium steady states
• mutual information
• entropy production
• stable noise