Large deviations, extremes and anomalous transport in non-equilibrium systems
The steady-state and dynamical properties of systems out of thermal equilibrium are currently a subject of intensive studies. They are typically characterized by generic long-range correlations and, unlike their equilibrium counterparts, no general theoretical framework exists. Nevertheless, considerable progress in understanding various aspects has been recently achieved either by detailed studies of simple, but representative, models, or by deriving general theorems such as fluctuation and work theorems, based mainly on symmetry considerations. We propose a one-week workshop within the framework of our already accepted Thematic Program on non-equilibrium systems at the Erwin Schrödinger Institute (ESI) in Vienna, during the period October 19, 2020 -November 13, 2020. The aim of the combined CECAM-ESI workshop is to bring together leading researchers, young scientists and students working on subjects of great current interest in non-equilibrium physics. The recent progress made in several subfields of this broad discipline makes our proposed workshop timely and highly promising. We plan to cover three main themes: Large deviations The large deviation function, apart from providing an accurate estimate of probabilities of rare events, has also been considered as a possible candidate for an effective free energy in out-of-equilibrium systems. Its calculation is technically challenging. Recently, there has been specific progress in three different contexts: (i) macroscopic fluctuation theory (MFT) exploiting hydrodynamic fluctuations, (ii) random matrix theory (RMT) which provides exact analytical tools, and (iii) exact results for the Kardar-Parisi-Zhang equation in one dimension describing fluctuating interfaces, directed polymers and Burger’s turbulence. Rare events: extremes and first-passage properties in stochastic processes Characterizing the statistics of rare events is an important issue in many areas of science (climate, finance). Extreme value statistics has also played an important role in statistical physics, in particular in the context of disordered and non-equilibrium complex systems. One of the major current issues is to understand the role of correlations between different degrees of freedom in characterizing the universality classes of extreme value distributions. There has been some recent progress in calculating the extreme value distributions exactly in some strongly correlated systems such as in RMT. Understanding general aspects of these extreme-value distributions remains a challenge. Anomalous transport in low-dimensional systems This highly-active field is concerned with transport in non-diffusive systems where energy or other conserved quantities are transported in a super-diffusive manner. This leads to a breakdown of Fourier’s law of heat transport and to anomalously large currents in low dimensions. Recently, important progress has been made whereby a general framework has been proposed for understanding anomalous transport in a broad class of systems. This framework - non-linear fluctuating hydrodynamics - provides a rather successful theoretical approach. This has generated considerable recent activity aiming at understanding the approximations involved and testing the general validity of this scheme. We expect that bringing together researchers from the above three sub-fields, where fluctuations and long-range correlations play crucial role, would generate new ideas and open up new directions of research.
Christoph Dellago (University of Vienna) - Organiser
Harald Posch (University of Vienna) - Organiser
Satya N. Majumdar (Universite de Paris-Sud) - Organiser
Gregory Schehr (Universite de Paris-Sud) - Organiser
David Mukamel (Weizmann Institute of Science) - Organiser