A preprint gives a counterexample to McKean’s conjecture for Landau–Coulomb dynamics

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Stable ID

math-mckean-landau-coulomb-counterexample-2026

Revision

math-mckean-landau-coulomb-counterexample-2026.v1

Field

Mathematics · Kinetic theory, partial differential equations and entropy

Evidence

Tier 1 · Peer reviewed: No

Record state

Provisional · Provisional claimed counterexample

Last checked

2026-09-04

AI role

The authors state that AI found the specific counterexample sequence. They rewrote the model’s convoluted proof and take responsibility for the mathematical arguments.

Record details

Problem or result

McKean’s proposed monotonic entropy-dissipation hierarchy for kinetic equations

Authors

Jonathan Junné, Raphael Winter and Havva Yoldaş

Institutions

University of Rennes–Inria–CNRS; Cardiff University; Delft University of Technology

Result date

First-version preprint submitted September 3, 2026

Why it matters

McKean’s conjecture is a proposed strengthening of Boltzmann’s H-theorem. A counterexample near equilibrium delineates exactly which higher-order monotonicity principles fail in physically important models.

Limits

This is a first-version, non-peer-reviewed preprint. The result concerns the homogeneous Landau–Coulomb equation and a grazing-collision Boltzmann regime; it does not invalidate the ordinary H-theorem, which only asserts monotonic entropy.

Sources

1. Primary: Junné, Winter and Yoldaş, Landau–Coulomb counterexample
2. Independent context: Silvestre, hard-sphere and Maxwell-molecule counterexamples

Correction and revision history

1. 2026-09-04 — Added after primary-source, scope, status, AI-role and limitation review.

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