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October 9, 2025Open Access

Mean-field approximation, Gibbs relaxation, and cross estimates

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Authors

ABArmand BernouUniversité Claude Bernard Lyon 1 MDMitia DuerinckxUniversité Paris-Sud

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Implication

This work reveals that cross error in chaos propagation and Gibbs relaxation is O(N^{-1}e^{-ct}) in Brownian systems, indicating enhanced mean-field approximation.

Key Points

The cross error between chaos propagation and Gibbs relaxation is O(N^{-1}e^{-ct}), demonstrating a high degree of accuracy.
An improved mean-field approximation error reduces from O(N^{-1}) to O(N^{-1}e^{-ct}) for one-particle density in translation-invariant systems.
The analysis employs the BBGKY hierarchy for correlation functions, applicable in both underdamped and overdamped Langevin dynamics.
New findings on Gibbs relaxation were developed alongside extensions beyond the weak interaction regime, ensuring broader applicability.

Cite This Study

Bernou et al. (2025) studied this question.

synapsesocial.com/papers/68e7f0af2d7e30942762c98f https://doi.org/10.48550/arxiv.2507.23123

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Implication

This work reveals that cross error in chaos propagation and Gibbs relaxation is O(N^{-1}e^{-ct}) in Brownian systems, indicating enhanced mean-field approximation.

Mean-field approximation, Gibbs relaxation, and cross estimates

Discussion

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Implication

Key Points

Cite This Study

Mean-field approximation, Gibbs relaxation, and cross estimates

Discussion

Member takes

Implication

Key Points

Cite This Study

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