Year: 2026
Type: preprint
Abstract: In 1966, McKean conjectured that the entropy production of Kac's caricature of a Maxwellian gas is nonincreasing in time \cite{McKean66}. We disprove this conjecture for the standard uniform-angle Kac equation. Our counterexamples are smooth, strictly positive, even mixtures of two Gaussians at different temperatures. We also show that every entropy derivative beyond the first violates its expected sign at some time along the same solution. The initial densities can be chosen with unit mass and second moment. mass and second moment.
Source: arXiv (Cornell University)
Author: Wang, Weinan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211989707