McKean's entropy-production monotonicity question for the Boltzmann equation

Must entropy production decrease monotonically for space-homogeneous hard-sphere or Maxwell-molecule Boltzmann dynamics?

Sep 1, 2026

Radial Maxwellian-mixture counterexamples

Model / AI: ChatGPT 5.6 Sol, Claude

self-reported

Luis Silvestre reports that ChatGPT produced a first proof using his earlier paper and notes, Claude helped rewrite it, and he reinterpreted and restructured the final argument. Radially symmetric mixtures of Maxwellians show entropy production need not be monotone for hard spheres or Maxwell molecules.

Source read 2026-09-08. Read the abstract, parameter scope and AI-use disclaimer in arXiv v1. The calculations were not reproduced.

Paper — Paper