Pith Number

pith:5WQBEDPC

pith:2026:5WQBEDPCGB3YXHHHQ6QDA3XGBV

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On the monotonicity of the entropy production in the Landau-Maxwell equation

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The entropy production of the homogeneous Landau-Maxwell equation becomes non-increasing after a finite time under well-distributed directional temperatures and sufficient moments.

arxiv:2601.03107 v3 · 2026-01-06 · math.AP

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Record completeness

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4 Citations open

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Claims

C1strongest claim

We study the homogeneous Landau equation with Maxwell molecules and prove that the entropy production is non-increasing provided the directional temperatures are well-distributed and the solution admits a moment of order ℓ, for some ℓ arbitrarily close to 2.

C2weakest assumption

The directional temperatures are well-distributed and the solution admits a moment of order ℓ arbitrarily close to 2; if this moment condition fails the monotonicity may not hold.

C3one line summary

Entropy production for the Landau equation with Maxwell molecules is non-increasing after a finite time under moment and temperature-distribution conditions, partially resolving a 1966 conjecture.

References

31 extracted · 31 resolved · 3 Pith anchors

[1] Fourier Transform Method in the Theory of the Boltzmann Equa- tion for Maxwellian Molecules 1975

[2] F.-U. Caja-Lopez, M. G. Delgadino, M.-P . Gualdani, and M. Taskovic.Contractivity of Wasserstein Distance and Exponential Decay for the Landau Equation with Maxwellian Molecules. Nov. 2025.DOI:10.4855 2025 · doi:10.48550/arxiv.2504.13802

[3] Propagation of Chaos for the Spatially Homogeneous Landau Equation for Maxwellian Molecules 2015 · doi:10.3934/krm.2016.9.1(cit

[4] José Antonio Carrillo and Shuchen Guo.From Fisher Information Decay for the Kac Model to the Landau-Coulomb Hierarchy. Feb. 2025.DOI:10 . 48550 / arXiv . 2502 . 18606. arXiv:2502.18606 [math](cit. on 2025

[5] On the Spatially Homogeneous Landau Equation for Hard Potentials Part Ii : H-Theorem and Applications 2000

Formal links

1 machine-checked theorem link

Cited by

1 paper in Pith

The entropy production is not always monotone in the space-homogeneous Boltzmann equation

Receipt and verification

First computed	2026-05-17T23:39:00.317184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eda0120de230778b9ce787a0306ee60d7fbb148af8a005facb5997ab6e937c7d

Aliases

arxiv: 2601.03107 · arxiv_version: 2601.03107v3 · doi: 10.48550/arxiv.2601.03107 · pith_short_12: 5WQBEDPCGB3Y · pith_short_16: 5WQBEDPCGB3YXHHH · pith_short_8: 5WQBEDPC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5WQBEDPCGB3YXHHHQ6QDA3XGBV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: eda0120de230778b9ce787a0306ee60d7fbb148af8a005facb5997ab6e937c7d

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "6e59c68f30f57849678a7b32a197ab780c0cd6dd2ffcad07a16bc840ada9bbbf",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-01-06T15:37:27Z",
    "title_canon_sha256": "0a6fa60a59e9ca56e86e708954b8a45da1229c9debce098633337953c5a5e4e4"
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  "schema_version": "1.0",
  "source": {
    "id": "2601.03107",
    "kind": "arxiv",
    "version": 3
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}