The Becker-Doring Process: Pathwise Convergence and Phase Transition Phenomena
| Autor: | Romain Yvinec, Erwan Hingant |
|---|---|
| Přispěvatelé: | Departamento de Matemática, Universidad del Bio Bio [Concepción] (UBB), Physiologie de la reproduction et des comportements [Nouzilly] (PRC), Institut National de la Recherche Agronomique (INRA)-Institut Français du Cheval et de l'Equitation [Saumur]-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Institut Français du Cheval et de l'Equitation [Saumur]-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Institut Français du Cheval et de l'Equitation [Saumur]-Institut National de la Recherche Agronomique (INRA) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
[SDV.OT]Life Sciences [q-bio]/Other [q-bio.OT]
Phase transition Stationary distribution Stochastic modelling [SDV]Life Sciences [q-bio] Process (computing) law of large numbers Statistical and Nonlinear Physics 01 natural sciences becker-döring 010305 fluids & plasmas 0103 physical sciences Convergence (routing) non-equilibrium potential Applied mathematics 010306 general physics infinite-dimensional reaction network entropy Becker-Doring Mathematics - Probability Mathematical Physics Mathematics |
| Zdroj: | Journal of Statistical Physics Journal of Statistical Physics, Springer Verlag, 2018, 177 (5), pp.506-527. ⟨10.1007/s10955-019-02377-2⟩ Journal of Statistical Physics, Springer Verlag, 2019, 177 (3), pp.506-527. ⟨10.1007/s10955-019-02377-2⟩ |
| ISSN: | 0022-4715 1572-9613 |
| Popis: | International audience; In this note, we prove alaw of large numbersfor an infinite chemical reactionnetwork for phase transition problems called the stochastic Becker-Döring process.Under a general condition on the rate constants we show the convergence in lawand pathwise convergence of the process towards the deterministic Becker-Döringequations. Moreover, we prove that the non-equilibrium potential, associated to thestationary distribution of the stochastic Becker-Döring process, approaches the rela-tive entropy of the deterministic limit model. Thus, the phase transition phenomenathat occurs in the infinite dimensional deterministic modelis also present in the finitestochastic model.In this note, we prove alaw of large numbersfor an infinite chemical reactionnetwork for phase transition problems called the stochastic Becker-Döring process.Under a general condition on the rate constants we show the convergence in lawand pathwise convergence of the process towards the deterministic Becker-Döringequations. Moreover, we prove that the non-equilibrium potential, associated to thestationary distribution of the stochastic Becker-Döring process, approaches the rela-tive entropy of the deterministic limit model. Thus, the phase transition phenomenathat occurs in the infinite dimensional deterministic modelis also present in the finitestochastic model. |
| Databáze: | OpenAIRE |
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