A 150-year-old mystery about how gas 'forgets' individual atoms to become a smooth breeze has finally been solved.
April 17, 2026
Original Paper
Propagation of chaos for the Boltzmann equation with very soft potentials
arXiv · 2604.13855
The Takeaway
Ludwig Boltzmann created the 'gas laws' in the 1800s, but there was a nagging mathematical hole for certain types of interactions. Mathematicians couldn't prove how individual, chaotic collisions between atoms settle into a predictable gas flow in every scenario. This paper finally closes that gap, proving the 'propagation of chaos' for the final remaining case. It is a foundational win that confirms our math for everything from airplane wings to weather patterns is actually solid. It is the ultimate proof that out of total microscopic chaos, perfect macroscopic order always emerges.
From the abstract
We build solutions to Kac's particle system and show that their empirical measures converge to the solution of the space-homogeneous Boltzmann equation in the regime of very soft potentials. This proves propagation of chaos for the last class of kernels for which it was still open. The proof relies on new estimates on the dissipation of the Fisher information along the Boltzmann equation, which allow us to control the strong singularities of the system. These estimates are obtained thanks to a n