Characteristic oscillations in frequency-resolved heat dissipation of linear time-delayed Langevin systems: Approach from the violation of the fluctuation-response relation

TL;DR

This paper analyzes the frequency-resolved heat dissipation in linear time-delayed Langevin systems, revealing characteristic oscillations linked to nonequilibrium features and providing a method to experimentally detect dissipation details.

Contribution

It introduces a frequency decomposition approach using the Harada-Sasa equality to analyze heat dissipation in time-delayed Langevin systems, highlighting oscillatory behaviors and extending to multiple delays.

Findings

Oscillatory behavior in heat dissipation spectrum.

High-frequency decay inversely proportional to frequency.

Low-frequency oscillation reflects heat dissipation magnitude and sign.

Abstract

Time-delayed effects are widely present in nature, often accompanied by distinctive nonequilibrium features, such as negative apparent heat dissipation. To elucidate detailed structures of the dissipation, we study the frequency decomposition of the heat dissipation in linear time-delayed Langevin systems. We decompose the heat dissipation into frequency spectrum using the Harada-Sasa equality, which relates the heat dissipation to the violation of the fluctuation-response relation (FRR). We find a characteristic oscillatory behavior in the spectrum, and the oscillation asymptotically decays with an envelope inversely proportional to the frequency in the high-frequency region. Furthermore, the oscillation over the low-frequency region reflects the magnitude and sign of the heat dissipation. We confirm the generality of the results by extending our analysis to systems with multiple delay times. Since the violation of FRR is experimentally accessible, our results suggest an experimental direction for detecting and analyzing detailed characteristics of dissipation in time-delayed systems.