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PreprintCC BY 4.0arXiv

Fluctuation--Response Relation in Finite-Size Noisy Coupled Phase Oscillators

  • Mrinal Sarkar
  • Yoshiyuki Y. Yamaguchi
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Abstract

Fluctuation--response relations (FRRs) provide a fundamental relation between spontaneous fluctuations and the linear response to external perturbations, yet their validity in non-equilibrium systems remains an open problem. In a general class of noisy, finite-size, mean-field models of coupled phase oscillators, we reveal two types of FRRs in the incoherent phase below the synchronization transition. The first, corresponding to the infinite-size limit (I-FRR), involves the convolution between the external force and the correlation function in the time domain. The second, the finite-size counterpart (F-FRR), is governed by finite-size fluctuations and carries a correction factor: a spectrum function whose roots correspond to eigenvalues, or Landau poles, of the linear operator. The finite-size fluctuations are suppressed in the weak-coupling or strong-noise limits, and F-FRR reduces to I-FRR. Our analytical findings are verified by extensive numerical simulations.

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Cite

BibTeXRIS
BibTeX
@misc{sarkar2026fluctuationresponse,
  title = {{Fluctuation--Response Relation in Finite-Size Noisy Coupled Phase Oscillators}},
  author = {Mrinal Sarkar and Yoshiyuki Y. Yamaguchi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28834},
  eprint = {2609.28834},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28834},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fluctuation--Response Relation in Finite-Size Noisy Coupled Phase Oscillators
AU  - Mrinal Sarkar
AU  - Yoshiyuki Y. Yamaguchi
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28834
UR  - https://arxiv.org/abs/2609.28834
AB  - Fluctuation--response relations (FRRs) provide a fundamental relation between spontaneous fluctuations and the linear response to external perturbations, yet their validity in non-equilibrium systems remains an open problem. In a general class of noisy, finite-size, mean-field models of coupled phase oscillators, we reveal two types of FRRs in the incoherent phase below the synchronization transition. The first, corresponding to the infinite-size limit (I-FRR), involves the convolution between the external force and the correlation function in the time domain. The second, the finite-size counterpart (F-FRR), is governed by finite-size fluctuations and carries a correction factor: a spectrum function whose roots correspond to eigenvalues, or Landau poles, of the linear operator. The finite-size fluctuations are suppressed in the weak-coupling or strong-noise limits, and F-FRR reduces to I-FRR. Our analytical findings are verified by extensive numerical simulations.
ER  -