The normal approximation to macroscopic dynamical fluctuations
Abstract
Under local detailed balance, the Lagrangian of macroscopic dynamical fluctuations has a canonical structure: its time-antisymmetric part is the entropy flux, and its time-symmetric part is a Legendre pair of kinetic and dissipation functions. We show what survives of that structure for normal (Gaussian) fluctuations around a nonequilibrium steady state. The quadratic Lagrangian keeps the canonical form, with the Hessian of the dissipation function as noise matrix. However, the force on the fluctuations differs from the linearized thermodynamic force by a term proportional to the driving and to the state dependence of the dynamical activity, so that local detailed balance is violated at the Gaussian level. Nevertheless, the Gaussian dynamics is gradient flow for the quadratic part of the nonequilibrium entropy, around an emergent nondissipative current. Finally, we show which parts of the Lagrangian can be reconstructed from measured Gaussian fluctuations.
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BibTeX
@misc{maes2026normal,
title = {{The normal approximation to macroscopic dynamical fluctuations}},
author = {Christian Maes and Kateřina Mladá and Karel Netočný},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03102},
eprint = {2611.03102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03102},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The normal approximation to macroscopic dynamical fluctuations
AU - Christian Maes
AU - Kateřina Mladá
AU - Karel Netočný
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03102
UR - https://arxiv.org/abs/2611.03102
AB - Under local detailed balance, the Lagrangian of macroscopic dynamical fluctuations has a canonical structure: its time-antisymmetric part is the entropy flux, and its time-symmetric part is a Legendre pair of kinetic and dissipation functions. We show what survives of that structure for normal (Gaussian) fluctuations around a nonequilibrium steady state. The quadratic Lagrangian keeps the canonical form, with the Hessian of the dissipation function as noise matrix. However, the force on the fluctuations differs from the linearized thermodynamic force by a term proportional to the driving and to the state dependence of the dynamical activity, so that local detailed balance is violated at the Gaussian level. Nevertheless, the Gaussian dynamics is gradient flow for the quadratic part of the nonequilibrium entropy, around an emergent nondissipative current. Finally, we show which parts of the Lagrangian can be reconstructed from measured Gaussian fluctuations.
ER -