Generalized fluctuation-dissipation theorem and Einstein relation in rotating equilibrium
Abstract
We derive a generalized fluctuation-dissipation theorem (FDT) for vector fields in rotating thermal equilibrium from an exact phase-space Kubo-Martin-Schwinger (KMS) relation. The resulting FDT contains rotation-induced tensorial contributions beyond a scalar thermal factor. In the local transport limit, we obtain a model-independent generalized Einstein relation with rotation in which, through second order in thermal vorticity, symmetric momentum diffusion depends on low-frequency spectral information beyond that encoded in the rotation-dependent dissipative drag. Remarkably, we find a new Einstein-type relation linking zero modes in the spectral function to the nonrotating drag coefficient. These zero modes underlie a new mechanism for the orbital polarization of heavy quarkonium. The same FDT constraint yields a modified detailed-balance relation whose first-order vortical correction is governed by transition polarization, without explicit dependence on the bath model. Our findings establish microscopic equilibrium constraints for studying rotating quantum matter in various fields.
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BibTeX
@misc{fang2026generalized,
title = {{Generalized fluctuation-dissipation theorem and Einstein relation in rotating equilibrium}},
author = {Shuo Fang and Shi Pu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01797},
eprint = {2610.01797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01797},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalized fluctuation-dissipation theorem and Einstein relation in rotating equilibrium
AU - Shuo Fang
AU - Shi Pu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01797
UR - https://arxiv.org/abs/2610.01797
AB - We derive a generalized fluctuation-dissipation theorem (FDT) for vector fields in rotating thermal equilibrium from an exact phase-space Kubo-Martin-Schwinger (KMS) relation. The resulting FDT contains rotation-induced tensorial contributions beyond a scalar thermal factor. In the local transport limit, we obtain a model-independent generalized Einstein relation with rotation in which, through second order in thermal vorticity, symmetric momentum diffusion depends on low-frequency spectral information beyond that encoded in the rotation-dependent dissipative drag. Remarkably, we find a new Einstein-type relation linking zero modes in the spectral function to the nonrotating drag coefficient. These zero modes underlie a new mechanism for the orbital polarization of heavy quarkonium. The same FDT constraint yields a modified detailed-balance relation whose first-order vortical correction is governed by transition polarization, without explicit dependence on the bath model. Our findings establish microscopic equilibrium constraints for studying rotating quantum matter in various fields.
ER -