## Abstract

We investigate the derivation of semilinear relaxation systems and scalar conservation laws from a class of stochastic interacting particle systems. These systems are Markov jump processes set on a lattice, they satisfy detailed mass balance (but not detailed balance of momentum), and are equipped with multiple scalings. Using a combination of correlation function methods with compactness and convergence properties of semidiscrete relaxation schemes we prove that, at a mesoscopic scale, the interacting particle system gives rise to a semilinear hyperbolic system of relaxation type, while at a macroscopic scale it yields a scalar conservation law. Rates of convergence are obtained in both scalings.

Original language | English (US) |
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Pages (from-to) | 715-763 |

Number of pages | 49 |

Journal | Journal of Statistical Physics |

Volume | 96 |

Issue number | 3-4 |

State | Published - Aug 1999 |

Externally published | Yes |

## Keywords

- Correlation function method
- Interacting particle systems
- Multiple scales
- Rates of convergence
- Relaxation systems
- Scalar conservation laws
- Semidiscrete schemes

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics