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DY: Fachverband Dynamik und Statistische Physik
DY 27: Statistical Physics far from Thermal Equilibrium - Part I
DY 27.3: Talk
Wednesday, March 18, 2015, 10:15–10:30, BH-N 334
Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model — •Valerio Lucarini1,2 and Giovanni Gallavotti3 — 1Institute of Meteorology, University of Hamburg, Hamburg, Germany — 2Department of Mathematics and Statistics, University of Reading, Reading, UK — 3Department of Physics, Sapienza University of Rome, Italy
We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive N-degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. The statistical properties of the irreversible and reversible model are in excellent agreement. The phase space contraction rate of the reversible model obeys the fluctuation relation. The equivalence between the two non-equilibrium ensembles extends to dynamical properties such as the Lyapunov exponents. These results have relevance in motivating the importance of the chaotic hypothesis, in explaining that we have the freedom to model non-equilibrium systems using different but equivalent approaches, and, in particular, that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties.