Blanc SIMI 1 - Sciences de l'information, de la matière et de l'ingénierie : Mathématiques et interactions

Interacting Particle Systems Out of Equilibrium – SHEPI

Submission summary

SHEPI is « un projet suite », after ANR LHMSHE (Limites hydrodynamiques et mécanique statistique hors équilibre ; coordination Thierry BODINEAU ; from 15/11/2007 to 2010). The involved research group has increased from 14 to 22 members.

The characterization and theoretical understanding of non-equilibrium phenomena forms one of the greatest challenges of current statistical physics and it sets many important mathematical problems. Our goal is to address further problems related to non-equilibrium, continuing the work of LHMSHE through induced new questions or problems still open on : A. thermal conductivity (Fourier's law) in lattice Hamiltonian dynamics like chains of oscillators or local collisional dynamics; B. non-equilibrium steady states (NESS), hydrodynamic limits, large deviations, for stochastic dynamics coming from Interacting Particle Systems (IPS); C. kinetically constrained models (KCM) and disordered systems.

A. Heat transport in lattice Hamiltonian dynamics

The latter is used to analyze the transfer of heat in materials having an order structure at the microscopic level, namely crystalline solids or materials which share features with solids and gases, e.g. aerogels. The corresponding models will be studied by perturbing or replacing deterministic interactions by random interactions which model the chaotic motions of individual components. Namely will be considered: Stochastic heat conduction models with random masses; local collisional dynamics; molecular dynamics simulations of non-equilibrium stationary states and thermal conductivity; weak coupling limits; Hamiltonian systems coupled to stochastic thermostats; the chain model.

B. Interacting particle systems, large deviations

Systems driven out of equilibrium through a field or through boundary conditions generically present a non zero current in the steady state. A first effective attempt for a nonequilibrium thermodynamical theory is to analyse stochastic microscopic models in contact with reservoirs. Questions to be studied in this direction will be : stationary large deviations in nonequilibrium stationary states (in particular with more than one stable point), fluctuations of the current, and phase transitions (in particular dynamical ones). We shall consider systems either with or without diffusion, with one or several conserved quantities. Hydrodynamic limits for a broad class of asymmetric systems will be studied through explicit couplings and attractiveness characterisations. Finally, we will consider long range models like sandpiles, Bak-Sneppen evolution, particles with long jumps, and also quasi-stationary processes.

C. Kinetically constrained dynamics and disordered systems

KCM are stochastic particle systems with Glauber or Kawasaki dynamics which have been introduced in the physics community to model the dynamics of liquids in the vicinity of the liquid glass transition. We will investigate for KCM: asymptotic behavior when dynamics starts far away from equilibrium; aging phenomena; relaxation to equilibrium of the East model; link between dynamical phase transition and glassy features.

For Glauber dynamics, we will study : the relaxation to equilibrium for disordered and non-disordered systems ; the dilute Ising model in the phase transition region. We will also consider : hydrodynamics and large deviations for particle systems with random field Kac interaction; site-disorder, hydrodynamics, and convergence to equilibrium for one-dimensional attractive asymmetric systems. Finally, analyzing the Kuramoto synchronization model we will examine biological models in the light of the recent advances in non-equilibrium statistical mechanics.


Project coordination

Ellen SAADA (UNIVERSITE PARIS DESCARTES) – ellen.saada@mi.parisdescartes.fr

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

MAP5, UPD and CNRS UNIVERSITE PARIS DESCARTES
DMA, ENS and CNRS CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE - DELEGATION REGIONALE ILE-DE-FRANCE SECTEUR PARIS B
LMRS, Univ. Rouen and CNRS CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE DELEGATION REGIONALE NORMANDIE

Help of the ANR 170,000 euros
Beginning and duration of the scientific project: - 36 Months

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