Nonequilibrium: Physics, Stochastics and Dynamical Systems

January 18-22, 2016
Statistical mechanics away from equilibrium is a field that is still in a formative stage in which general concepts slowly emerge. One of the major difficulties is to understand which aspects of the theory are model-dependent and which ones are universal. In the modeling of nonequilibrium both deterministic and stochastic models are used. It is one of the aims of the workshop to represent both approaches and create communication between them.

This conference will gather a mixed audience composed of mathematicians and theoretical physicists. We believe that carefully chosen mini-courses can be of great use not only for graduate students, but also for researchers who became more and more specialized due to the complexity of this field.

We shall mainly focus on classical deterministic systems and stochastic systems such as interacting particle systems. Besides we want to organize one specific day focused on three specialized themes namely: KPZ universality, self-organized criticality and the Boltzmann equation.

The two basic paradigms for deterministic (dynamical system) non-equilibrium statistical mechanics are the so-called thermostated systems and open systems.
Thermostated systems are Hamiltonian systems (with finitely many degrees of freedom) driven away from equilibrium by an external (non-Hamiltonian) force and constrained by a deterministic thermostating force to stay on a surface of constant energy.
Open systems are Hamiltonian systems consisting of a « small » Hamiltonian system (with finitely many degrees of freedom) interacting with, say two, ‘large’ reservoirs which are infinitely extended Hamiltonian systems. The reservoirs are initially in thermal equilibrium at distinct temperatures and the temperature differential leads to a steady heat flux from the hotter to the colder reservoir across the small system.

A more abstract approach consists in describing the microscopic time evolution by a general smooth dynamical system, identify nonequilibrium steady states (NESS), and study how these vary under perturbations of the dynamics.
Another important role is played by the so-called Fluctuation Theorems, such as the Evans-Searles and Gallavotti-Cohen Fluctuation Theorems, related to entropy production.

Another modeling of nonequilibrium consists in introducing stochasticity in the micro-dynamics. This leads to markovian models of interacting particles driven by reservoirs and/or bulk forces.  In this context, there are exactly solvable models, such as the symmetric and asymmetric exclusion processes coupled to boundary reservoirs, where one can explicitly compute correlations in the NESS. There is also a general macroscopic approach in which one studies the fluctuations of the density profiles in non-equilibrium, via the theory of hydrodynamic limits and associated large deviations.

Scientific & Organizing Committee

Jean-René Chazottes (CNRS & Ecole polytechnique)
Frank Redig (TU Delft)


Large time asymptotics of small perturbations of a deterministic dynamics of hard spheres

Classical versus quantum equilibrium

Models for evolution and selection

Slow heating and localization effects in quantum dynamics

  • Deepak Dhar (Tata Institute of Fundamental Research Mumbai)

Pattern formation in growing sandpiles

TASEP Hydrodynamics using microscopic characteristics

Macroscopic fluctuation theory [Mini-course]

Random matrices and rarefied gases properties

Asymmetric dualities in non-equilibrium systems

Metastability in a condensing zero-range process in the thermodynamic limit

The weak KPZ univers
ality conjecture

Renormalization group and stochastic PDE’s

Quantitative analysis of Clausius inequality in driven diffusive systems
and corrections to the hydrodynamic limit

Hydrodynamic spectrum and dynamical phase transition in one-dimensional bulk-driven particle gases

Threshold state of the abelian sandpile

Nonequilibrium physics [Mini-course]

Nonequilibrium generalization of the Nernst’s heat theorem

Latent heat and the Fourier law

Generalized detailed balance and biological applications

Determinantal structures for 1D KPZ equation and related models