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PreprintCC BY 4.0arXiv

Formal Fluctuation-Response Relations for Non-Stationary Systems: The Dynamic Conjugate Variable

  • Igor M. Sokolov
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Abstract

Fluctuation-response relations (FRRs) connect the linear response of a system to an external perturbation with properties of spontaneous fluctuations in the unperturbed system. We provide a simple derivation of FRRs for non-stationary dynamics following an almost standard way based on introducing a variable conjugated to perturbation (a dynamic conjugate). The derivation relies solely on the Markovianity of the underlying dynamics, with the only additional assumption that the transition PDF of the process is differentiable with respect to the strength of a constant, time- independent perturbation. The structure of this conjugate variable is however unusual: it is a two-time one, and reduces to a usual single-time conjugate in stationary situations. We show how several known results follow from this approach.

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Cite

BibTeXRIS
BibTeX
@misc{sokolov2026formal,
  title = {{Formal Fluctuation-Response Relations for Non-Stationary Systems: The Dynamic Conjugate Variable}},
  author = {Igor M. Sokolov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20525},
  eprint = {2609.20525},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20525},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Formal Fluctuation-Response Relations for Non-Stationary Systems: The Dynamic Conjugate Variable
AU  - Igor M. Sokolov
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20525
UR  - https://arxiv.org/abs/2609.20525
AB  - Fluctuation-response relations (FRRs) connect the linear response of a system to an external perturbation with properties of spontaneous fluctuations in the unperturbed system. We provide a simple derivation of FRRs for non-stationary dynamics following an almost standard way based on introducing a variable conjugated to perturbation (a dynamic conjugate). The derivation relies solely on the Markovianity of the underlying dynamics, with the only additional assumption that the transition PDF of the process is differentiable with respect to the strength of a constant, time- independent perturbation. The structure of this conjugate variable is however unusual: it is a two-time one, and reduces to a usual single-time conjugate in stationary situations. We show how several known results follow from this approach.
ER  -