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.
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 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
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
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
Renormalization group and stochastic PDE’s
Quantitative analysis of Clausius inequality in driven diffusive systems
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