MATHPHTopic
Kinetic and fluid equations from particle dynamics
The Boltzmann equation describes a gas through the statistics of molecular collisions, and fluid equations follow from it; deriving both from Newton's laws for individual molecules is Hilbert's sixth problem. For a gas of hard spheres a derivation was posted in 2025 (Deng, Hani and Ma) and is under review, while other physically central cases remain unproven.
Why it matters
These derivations are the logical link between reversible microscopic mechanics and the irreversible macroscopic equations used across physics.
Review
Y. Deng, Z. Hani, X. Ma, Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory, arXiv, 2025. https://arxiv.org/abs/2503.01800 reference checked
Proof
- Signed record
- 43f072b403d6…
- Public log
- Entry 262, in checkpoint 2,123
- Bitcoin date
- Block 969,698, 2026-10-03