Local Detailed Balance in the Lorenz Model: Replaces the Butterfly with Frenetic Bursting
Abstract
The Lorenz system is the canonical low-order model of convective instability, yet its dissipative and driving terms have never been checked against, nor constructed from, an explicit thermodynamic bookkeeping. We derive a modification that satisfies the local-detailed-balance condition for macroscopic relaxation toward nonequilibrium steady states, thereby identifying the thermodynamic force, entropy-production rate and frenesy of the resulting flow. The resulting model produces a transition from a quiescent fixed point to a robust, large-amplitude relaxation oscillation, closely analogous to recharge-discharge oscillator paradigms used for the El Nino-Southern Oscillation. The system alternates between a long, nearly reversible recharge phase and a brief, violently frenetic discharge burst, during which essentially all of the cycle's activity and entropy production is concentrated.
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BibTeX
@misc{khodabandehlou2026local,
title = {{Local Detailed Balance in the Lorenz Model: Replaces the Butterfly with Frenetic Bursting}},
author = {Faezeh Khodabandehlou and Christian Maes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21415},
eprint = {2609.21415},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21415},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local Detailed Balance in the Lorenz Model: Replaces the Butterfly with Frenetic Bursting
AU - Faezeh Khodabandehlou
AU - Christian Maes
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21415
UR - https://arxiv.org/abs/2609.21415
AB - The Lorenz system is the canonical low-order model of convective instability, yet its dissipative and driving terms have never been checked against, nor constructed from, an explicit thermodynamic bookkeeping. We derive a modification that satisfies the local-detailed-balance condition for macroscopic relaxation toward nonequilibrium steady states, thereby identifying the thermodynamic force, entropy-production rate and frenesy of the resulting flow. The resulting model produces a transition from a quiescent fixed point to a robust, large-amplitude relaxation oscillation, closely analogous to recharge-discharge oscillator paradigms used for the El Nino-Southern Oscillation. The system alternates between a long, nearly reversible recharge phase and a brief, violently frenetic discharge burst, during which essentially all of the cycle's activity and entropy production is concentrated.
ER -