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.
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. Gonēalves, 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 noiseand non-conservative force.- T. Leličvre,
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.
