dorsal/arxiv
View SchemaDiscreteness-induced Stochastic Steady State in Reaction Diffusion Systems: Self-consistent Analysis and Stochastic Simulations
| Authors | Yuichi Togashi, Kunihiko Kaneko |
|---|---|
| Categories | |
| ArXiv ID | physics/0409027 |
| URL | https://arxiv.org/abs/physics/0409027 |
| DOI | 10.1016/j.physd.2004.12.008 |
| Journal | Physica D 205, 87 (2005) |
Abstract
A self-consistent equation to derive a discreteness-induced stochastic steady state is presented for reaction-diffusion systems. For this formalism, we use the so-called Kuramoto length, a typical distance over which a molecule diffuses in its lifetime, as was originally introduced to determine if local fluctuations influence globally the whole system. We show that this Kuramoto length is also relevant to determine whether the discreteness of molecules is significant or not. If the number of molecules of a certain species within the Kuramoto length is small and discrete, localization of some other chemicals is brought about, which can accelerate certain reactions. When this acceleration influences the concentration of the original molecule species, it is shown that a novel, stochastic steady state is induced that does not appear in the continuum limit. A theory to obtain and characterize this state is introduced, based on the self-consistent equation for chemical concentrations. This stochastic steady state is confirmed by numerical simulations on a certain reaction model, which agrees well with the theoretical estimation. Formation and coexistence of domains with different stochastic states are also reported, which is maintained by the discreteness. Relevance of our result to intracellular reactions is briefly discussed.
{
"annotation_id": "948f7cc9-d64c-408c-b388-e37ac8501613",
"date_created": "2026-03-02T18:00:53.678000Z",
"date_modified": "2026-03-02T18:00:53.678000Z",
"file_hash": "fb05dd89159b51666fc17b9979dfbc9f95ec48b1a525e60a26a059b48c44c70c",
"private": false,
"record": {
"abstract": "A self-consistent equation to derive a discreteness-induced stochastic steady\nstate is presented for reaction-diffusion systems. For this formalism, we use\nthe so-called Kuramoto length, a typical distance over which a molecule\ndiffuses in its lifetime, as was originally introduced to determine if local\nfluctuations influence globally the whole system. We show that this Kuramoto\nlength is also relevant to determine whether the discreteness of molecules is\nsignificant or not. If the number of molecules of a certain species within the\nKuramoto length is small and discrete, localization of some other chemicals is\nbrought about, which can accelerate certain reactions. When this acceleration\ninfluences the concentration of the original molecule species, it is shown that\na novel, stochastic steady state is induced that does not appear in the\ncontinuum limit. A theory to obtain and characterize this state is introduced,\nbased on the self-consistent equation for chemical concentrations. This\nstochastic steady state is confirmed by numerical simulations on a certain\nreaction model, which agrees well with the theoretical estimation. Formation\nand coexistence of domains with different stochastic states are also reported,\nwhich is maintained by the discreteness. Relevance of our result to\nintracellular reactions is briefly discussed.",
"arxiv_id": "physics/0409027",
"authors": [
"Yuichi Togashi",
"Kunihiko Kaneko"
],
"categories": [
"physics.chem-ph",
"nlin.PS",
"physics.bio-ph",
"q-bio.SC"
],
"doi": "10.1016/j.physd.2004.12.008",
"journal_ref": "Physica D 205, 87 (2005)",
"title": "Discreteness-induced Stochastic Steady State in Reaction Diffusion Systems: Self-consistent Analysis and Stochastic Simulations",
"url": "https://arxiv.org/abs/physics/0409027"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "fb3bae70-51f1-4ab9-8def-c89c3f5127cc",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}