### Séminaire de groupe

Foundations of the local equilibrium concept |

Rudolf Hilfer |

ICP, Universite de Stuttgart (Allemagne) |

jeudi 16 novembre 2017 , 10h25 |

Salle de séminaire du groupe de Physique Statistique |

Local equilibrium states change slowly in time because they are almost stationary. As a consequence, local equilibrium states have to be related to local states that are time-invariant. It is held in the literature that a proper mathematical formulation of local equilibrium states must start from the class of time-invariant measures for infinitely extended systems [1]. This presentation argues that the set of time-invariant measures of infinite systems is too small [2]. A suitable extension are states of bounded mean oscillation (BMO-states) that are also close to time-invariant states. BMO-states are states for which the expectation values of all observables are functions of bounded mean oscillation in time. Results for long-time scaling limits of induced time flows on subsets of BMO-states then provide the mathematical foundation for the local equilibrium concept. <\br><\br> [1] H. Spohn, Large Scale Dynamics of Interacting Particles, 1991 <\br> [2] R. Hilfer, Analysis, 36, 49-64 (2016) |