Stochastic Dynamics Out of Equilibrium

Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments.

It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown.

The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics.

The present volume is indispensable reading for researchers and Ph.D. students working in such areas.

Inhalt

Part I: Mini-courses of the pre-school at CIRM, P. Dai Pra, Stochastic mean-field dynamics and applications to life sciences.- P. Degond, A. Frouvelle, S. Merino-Aceituno and A. Trescases, Alignment of self-propelled rigid bodies: from particle systems to macroscopic equations.- G. Schütz, Fluctuations in Stochastic Interacting Particle Systems.- *Part II: Mini-courses at IHP, P. Gonçalves, Hydrodynamics for symmetric exclusion in contact with reservoirs.- F. Rezakhanlou, Stochastic Solutions to Hamilton-Jacobi Equations.- Part III: Workshop 1: Numerical aspects of nonequilibrium dynamics, F. Achleitner, A. Arnold and B. Signorello, On Optimal Decay Estimates for ODEs and PDEs with Modal Decomposition.- O. Kebiri, L. Neureither and C. Hartmann, Adaptive importance sampling with forward-backward stochastic differential equations.- B. Leimkuhler and M. Sachs, Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force.- T. Lelièvre, Dorian Le Peutrec and B. Nectoux, Exit event from a metastable state and Eyring-Kramers law for the overdamped Langevin dynamics.- S. Lepri, Collisional relaxation and dynamical scaling in multiparticle collisions dynamics.- P. Monmarché, A short introduction to Piecewise Deterministic Markov samplers.- L. Neureither and C. Hartmann, Time scales and exponential trend to equilibrium: Gaussian model problems.- *Part IV: Workshop 2: Life sciences, L. L. Bonilla, M. Carretero and F. Terragni, Stochastic models of blood vessel growth.- R. Schinazi, Survival under high mutation.- Y. Xu, R. Mei, Y. Li and J. Kurths, Particle transport in a confined ratchet driven by the colored noise.- A. Frouvelle and Jian-Guo Liu, Long-time dynamics for a simple aggregation equation on the sphere.- *Part V: Workshop 3: Stochastic dynamics out of equilibrium, G. Barraquand and M. Rychnovsky, Tracy-Widom asymptotics for a river delta model.- A. De Masi, P.A. Ferrari, E. Presutti and N. Soprano-Loto, Hydrodynamics of the N-BBM process.- A. Faggionato, 1D Mott variable-range hopping with external field.- T. Funaki, Invariant measures in coupled KPZ equations.- G. Gallavotti, Reversible Viscosity and Navier-Stokes Fluids.- S. Goldstein, D. Huse, J. Lebowitz and P. Sartori, On the nonequilibrium entropy of large and small systems.- H. Lacoin, Marginal relevance for the $\gamma$-stable pinning model.- T. Mountford and Glauco Valle, A rate of convergence result for the Frederickson-Andersen model.- F. Redig* and F. Sau, Stochastic duality and eigenfunctions.