Planckian dissipation from classical hydrodynamics
Abstract
Hydrodynamics describes the long-time, long-distance dynamics of interacting quantum systems by classical equations, yet at low temperature quantum fluctuations might eventually invalidate this classical picture. Here we ask what it takes for a quantum system to sustain a consistently classical hydrodynamic description. Our starting point is the quantum fluctuation-dissipation theorem which, when read in the time domain, acts as a blurring of the fine details of correlation functions on a Planckian time-scale. We analyse how this blurring interacts with the diffusive large-deviation form of correlators assuming the existence of a hydrodynamic light cone velocity, and show that the interior of the cone splits into a classical region, where correlation and response satisfy the classical fluctuation-dissipation relation, and a quantum region, where they deviate sharply from it. We illustrate the mechanism on three phenomenological hydrodynamic equations - diffusion, telegraph and diffusive-telegraph. Preserving a finite classical region as the temperature is lowered forces the current relaxation rate to be bounded from above by the Planckian rate. This bound connects to bounds on diffusivity, equilibration time and shear viscosity. In this way, a Planckian bound on dissipation emerges not as a quantum constraint on microscopic dynamics, but as the price a system pays to remain describable by classical hydrodynamics down to low temperatures.
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BibTeX
@misc{foini2026planckian,
title = {{Planckian dissipation from classical hydrodynamics}},
author = {Laura Foini and Jorge Kurchan and Silvia Pappalardi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.19450},
eprint = {2605.19450},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19450},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Planckian dissipation from classical hydrodynamics
AU - Laura Foini
AU - Jorge Kurchan
AU - Silvia Pappalardi
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2605.19450
UR - https://arxiv.org/abs/2605.19450
AB - Hydrodynamics describes the long-time, long-distance dynamics of interacting quantum systems by classical equations, yet at low temperature quantum fluctuations might eventually invalidate this classical picture. Here we ask what it takes for a quantum system to sustain a consistently classical hydrodynamic description. Our starting point is the quantum fluctuation-dissipation theorem which, when read in the time domain, acts as a blurring of the fine details of correlation functions on a Planckian time-scale. We analyse how this blurring interacts with the diffusive large-deviation form of correlators assuming the existence of a hydrodynamic light cone velocity, and show that the interior of the cone splits into a classical region, where correlation and response satisfy the classical fluctuation-dissipation relation, and a quantum region, where they deviate sharply from it. We illustrate the mechanism on three phenomenological hydrodynamic equations - diffusion, telegraph and diffusive-telegraph. Preserving a finite classical region as the temperature is lowered forces the current relaxation rate to be bounded from above by the Planckian rate. This bound connects to bounds on diffusivity, equilibration time and shear viscosity. In this way, a Planckian bound on dissipation emerges not as a quantum constraint on microscopic dynamics, but as the price a system pays to remain describable by classical hydrodynamics down to low temperatures.
ER -