Fifth-order ATP reaction-diffusion entropy obstruction

We construct smooth, strictly positive concentration profiles for the six-species reversible fifth-order ATP-style reaction in three spatial dimensions. Every species retains exactly its equilibrium spatial mean, while relative entropy and instantaneous diffusion and chemical entropy dissipation tend to zero and the L1 norm of the net mass-action reaction source diverges. This provides a static obstruction to bounding instantaneous reaction sources using only conserved masses and instantaneous entropy/dissipation. It does not establish finite-time blow-up or resolve the open problem of global deterministic classical regularity. Connections to prior entropy-dissipation theory are stated in the paper.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23949846
Primary Topic
Nonlinear Partial Differential Equations
Type
preprint
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preprint

Fifth-order ATP reaction-diffusion entropy obstruction

Kias Henry
Zenodo (CERN European Organization for Nuclear Research)
Nonlinear Partial Differential Equations
preprint

Fifth-order ATP reaction-diffusion entropy obstruction

Kias Henry
preprint en

Abstract

We construct smooth, strictly positive concentration profiles for the six-species reversible fifth-order ATP-style reaction in three spatial dimensions. Every species retains exactly its equilibrium spatial mean, while relative entropy and instantaneous diffusion and chemical entropy dissipation tend to zero and the L1 norm of the net mass-action reaction source diverges. This provides a static obstruction to bounding instantaneous reaction sources using only conserved masses and instantaneous entropy/dissipation. It does not establish finite-time blow-up or resolve the open problem of global deterministic classical regularity. Connections to prior entropy-dissipation theory are stated in the paper.

Zenodo (CERN European Organization for Nuclear Research)
Nonlinear Partial Differential Equations
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Fifth-order ATP reaction-diffusion entropy obstruction — Kias Henry · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS