# Timetable (PDSW02)

## Nonequilibrium Dynamics of Interacting Particle Systems

Monday 27th March 2006 to Friday 7th April 2006

 08:30 to 09:55 Registration 10:00 to 11:00 B Derrida ([ENS, Paris])Fluctuations and large deviations in non-equilibrium systems: Lecture I The exact solutions of simple models allow us to obtain the large deviation functions of density profiles and of the current through simple systems in contact with two reservoirs at different densities. These simple models show that non-equilibrium systems have a number of properties which contrast with equilibrium systems: phase transitions in one dimension, non local free energy functional, violation of the Einstein relation between the compressibility and the density fluctuation, non-Gaussian density fluctuations. They also lead to a general expression for the current fluctuations through a diffusive system in contact with two reservoirs. B Derrida, J L Lebowitz, E R Speer Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case Phys. Rev. Lett. 87, 150601 (2001) B Derrida, B Doucot, P-E Roche, Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries J. Stat. Phys. 115, 717-748 (2004) T. Bodineau, B Derrida Current fluctuations in non-equilibrium diffusive systems: an additivity principle Phys. Rev. Lett. 92, 180601 (2004) INI 1 , 11:00 to 11:30 Coffee 11:30 to 12:30 DJ Evans (Australian National University)The fluctuation and nonequilibrium free energy theorems, Theory and experiment: Lecture I 1. We give a brief summary of the derivations of the Evans-Searles Fluctuation Theorems (FTs) and the NonEquilibrium Free Energy Theorems (Crooks and Jarzynski). The discussion is given for time reversible Newtonian dynamics. We emphasize the role played by thermostatting. We also highlight the common themes inherent in the Fluctuation and Free Energy Theorems. We discuss a number of simple consequences of the Fluctuation Theorems including the Second Law Inequality, the Kawasaki Identity and the fact that the dissipation function which is the subject of the FT, is a nonlinear generalization of the spontaneous entropy production, that is so central to linear irreversible thermodyanamics. Lastly we give a brief update on the latest experimental tests of the FTs (both steady state and transient) and the NonEquilibrium Free Energy Theorem, using optical tweezer apparatus. 2 The Fluctutation Theorem: In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in small thermostatted nonequilibrium systems which are observed for a short period of time. This Theorem places quantitative restrictions on the operation of small (nano) machines and devices. These constraints cannot be circumvented. Quantitative predictions made by the Fluctuation Theorem regarding the probability of Second Law violations' have been confirmed experimentally, both using molecular dynamics computer simulation and very recently in two laboratory experiments[1] which employed optical tweezers. In this talk we give a brief summary of the theory [2] and a description of the experiments. References [1] Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales, by Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J. and Evans, D.J., Phys. Rev. Lett., 89 (5), 050601/1?4 (2002). [2] The Fluctuation Theorem by Denis J Evans and Debra J Searles, Advances in Physics, 51 , 1529-1585(2002). INI 1 , 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 Poster session I 15:00 to 15:30 Tea 15:30 to 16:30 GM Schuetz ([Juelich])Hydrodynamic limit for driven diffusive systems: Lecture I The large scale behaviour of microscopic stochastic particle systems can often be described in tems of nonlinear partial differential equations which can be predicted phenomenologically or sometimes derived rigorously using probabilistic tools. For one-component systems this allows not only for computing the (deterministic) space-time evolution of the coarse-grained local order parameter, but also for the derivation of the stationary phase diagram in bulk-driven finite systems with open boundaries. The Bethe ansatz provides the means to study fluctuations on finer scales. Systems with two or more components exhibit richer physics, but the theory is far less developed, both mathematically from a probabilistic and PDE point of view and from a statistical physics perspective. Focussing on paradigmatic one-dimensional lattice gas models for driven diffusive systems far from thermal equilibrium the lecture aims at giving a non-technical overview of some well-known rigorous and some more recent numerically established results for one-component systems with conserved particle dynamics or with slow reaction kinetics and at highlighting some aspects of the present incomplete state of art for two-component systems which deserve further investigation. INI 1 16:30 to 17:30 H Hinrichsen ([Wuerzburg])Absorbing state phase transitions: Lecture I The purpose of these lectures is to give a basic introduction to the physics of phase transitions far from equilibrium. Starting with a general introduction to non-equilibrium statistical mechanics four different topics will be addressed. At first the universality class of directed percolation will be discussed, which plays a fundamental role in non-equilibrium statistical physics. The second part concerns the properties of other universality classes which have been of interest in recent years. The third part deals with phase transitions in models with long-range interactions, including memory effects and so-called Levy-flights. Finally, deposition-evaporation phenomena leading to wetting transitions out of equilibrium will be reviewed. INI 1 , 17:30 to 18:30 Wine Reception 18:45 to 19:30 Dinner at Wolfson Court (Residents Only)