Regensburg 2013 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 18: Statistical Physics Far from Thermal Equilibrium
DY 18.7: Vortrag
Mittwoch, 13. März 2013, 11:15–11:30, H48
Crooks’ Fluctuation Theorem for a Process on a 2D Fluid Field — •Julia Gundermann1, Jochen Bröcker2, and Holger Kantz1 — 1Max Planck Institute for the Physics of Complex Systems, Dresden, Germany — 2Department of Meteorology, University of Reading, UK
We investigate the behavior of two-dimensional inviscid and incompressible flow when pushed out of dynamical equilibrium. We use the 2D vorticity equation with spectral truncation on a rectangular domain. For sufficiently large number of degrees of freedom, the equilibrium statistics of the flow can be described through a canonical ensemble approach with two conserved quantities, energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. We interpret this as doing work to the system. Evolving along a forward and its corresponding backward process, we show that the statistics of the work performed satisfies Crooks’ relation Pf(W)/Pb(−W) = eβ (W−Δ F). The parameters Δ F and β are given by the formal analogy with the canonical ensemble as the free energy difference and, respectively, the inverse temperature 1/kB T.