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

Xin Wang1,*, Ruicheng Bao2, and Naruo Ohga2

  • 1Department of Physics, Graduate School of Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8574, Japan
  • 2Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

  • *Contact author: wangxin579@outlook.com
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Phys. Rev. Research 8, 013039 – Published 15 January, 2026

DOI: https://doi.org/10.1103/x2dm-9p8m

Abstract

Time-delayed effects are widely present in nature, often accompanied by distinctive nonequilibrium features, such as net heat flow from a single thermal bath to the system. 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.

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Phys. Rev. Research 8, 013039– Published 15 January, 2026
  • Received 4 April 2025
  • Accepted 17 December 2025
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