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

Matthias Carosi, Ot Garcés, Adrià Garcés, Demian Levis

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 $ψ^4$ 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.

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

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 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.
Paper Structure (13 sections, 77 equations, 2 figures)

This paper contains 13 sections, 77 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Non-Hermitian Model A dynamics
  3. Quantifying irreversibility via FDT violations
  4. Response-field formalism and generating functional
  5. Time-reversal symmetry as an equilibrium symmetry
  6. Small-noise expansion about a stationary solution
  7. Harada-Sasa relation for entropy production
  8. Entropy Production rate from the Langevin equation
  9. Local EPR as a generic mode expansion
  10. Local EPR of a uniform state
  11. Application to the Non-Reciprocal Model A
  12. Local EPR across a domain wall
  13. Conclusions

Figures (2)

  • Figure 1: The average LEPR due to the domain wall for $d=2$. The momentum components $\sigma_p$ as defined in Eq. \ref{['eqn:LEPR_DW_p_component']} are shown for some values of the dimensionless momentum $p=q_\parallel/\alpha$.
  • Figure 2: Left: Schematic representation of the domain-wall and vision-cone set-up. Right: The average LEPR due to the presence of the domain wall for various values of the tilt angle $\theta_{\mathbf v}$.