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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.12390 |
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Table of Contents:
- We calculate transport coefficients from the Chapman--Enskog expansion with BGK collision operators, obtaining exactly $κ= \frac{5nT}{2mν}$, and show that maximum entropy closure yields identical results when applied with the same collision operator. Through structural arguments, we suggest that this $1/ν$ divergence extends to other local collision operators of the form $\mathcal{L} = ν\hat{L}$, making the divergence fundamental to the Chapman--Enskog approach rather than a closure artifact. To address this limitation, we propose a phenomenological effective collision frequency $ν_{\eff} = ν\sqrt{1 + \Kn^2}$ motivated by gradient-driven decorrelation, where $\Kn$ is the Knudsen number. We verify that this regularization maintains conservation laws and thermodynamic consistency while yielding finite transport coefficients across all collisionality regimes. Comparison with exact solutions of a bounded kinetic model shows similar functional form, providing limited validation of our approach. This work provides explicit calculation of a known divergence problem in kinetic theory and offers one phenomenological regularization method with transparent treatment of mathematical assumptions versus physical approximations.