Onsager symmetry for systems with broken time-reversal symmetry

TL;DR

This paper demonstrates through numerical and analytical methods that Onsager symmetry persists in systems with spatially varying magnetic fields, even when time-reversal symmetry is broken, expanding understanding of non-equilibrium thermodynamics.

Contribution

The paper provides the first numerical evidence and an analytical derivation showing Onsager symmetry holds in systems with spatially dependent magnetic fields.

Findings

Onsager symmetry remains valid with spatially varying magnetic fields

Analytical proof for one-dimensional magnetic field variation

Qualitative explanation for the generic case

Abstract

We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength varies only in one direction, we analytically derive the result. For the generic case, a qualitative explanation is provided.