Time irreversibility and entropy production in non-Hermitian Model A field theories

TL;DR

This paper introduces a framework to quantify irreversibility and entropy production in non-Hermitian scalar field theories, revealing how anti-Hermitian components influence fluctuation-dissipation violations and entropy generation.

Contribution

It develops a systematic method using stochastic path integrals to compute entropy production and FDT violations in non-Hermitian Model A theories, with explicit applications to non-reciprocal Ginzburg-Landau models.

Findings

Local entropy production is determined by the anti-Hermitian part of the Langevin equation.

Non-Hermitian terms cause linear FDT violations and quadratic entropy production.

Entropy production localizes at interfaces in non-uniform states.

Abstract

We develop a systematic framework to quantify irreversibility in scalar Model A field theories with a generic non-Hermitian term driving the dynamics. Using the stochastic path-integral formalism, we perform a controlled small-noise expansion, allowing the computation of the entropy production rate (EPR) and violations of the fluctuation-dissipation theorem (FDT). We show that the local EPR is entirely determined by the anti-Hermitian part of the linearised Langevin equation. Around steady states, the non-Hermitian component produces linear corrections to FDT violations and contributes quadratically to the EPR. As an illustration of the applicability of our approach, we analyse a minimal non-Hermitian extension of the Ginzburg-Landau $\psi^4$ theory describing a non-reciprocal Ising model at coarse-grained scales, for which we obtain explicit expressions of the local EPR, showing that it localises at interfaces in non-uniform states. Our results provide a general characterisation of TRS breaking in non-Hermitian scalar field theories.