Kinetic and fluid equations from particle dynamics
This text mentions work from 2024 on. Those parts were partly written without a live literature search and have not been checked by an editor yet.
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
Timestamp record
- Signed record
- 43f072b403d6…
- Public log
- Entry 262, in checkpoint 2,123
- In the log by
- Block 969,698, 2026-10-03
This text was in the PubPhys log by that date. The date says nothing about when the problem was first posed.