Mielke, Alexander and Stephan, Artur
(2020)
*Coarse-graining via EDP-convergence for linear fast-slow reaction systems.*
Mathematical Models and Methods in Applied Sciences, 30
(9).
pp. 1765-1807.

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614kB |

Official URL: https://doi.org/10.1142/S0218202520500360

## Abstract

We consider linear reaction systems with slow and fast reactions, which can be interpreted as master equations or Kolmogorov forward equations for Markov processes on a finite state space. We investigate their limit behavior if the fast reaction rates tend to infinity, which leads to a coarse-grained model where the fast reactions create microscopically equilibrated clusters, while the exchange mass between the clusters occurs on the slow time scale. Assuming detailed balance the reaction system can be written as a gradient flow with respect to the relative entropy. Focusing on the physically relevant cosh-type gradient structure we show how an effective limit gradient structure can be rigorously derived and that the coarse-grained equation again has a cosh-type gradient structure. We obtain the strongest version of convergence in the sense of the Energy-Dissipation Principle (EDP), namely EDP-convergence with tilting.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2661 |

Deposited By: | Monika Drueck |

Deposited On: | 17 Jan 2022 16:36 |

Last Modified: | 24 Jan 2022 15:26 |

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