title: Crooks fluctuation theorem for a process on a two-dimensional fluid field.
abstract: We investigate the behavior of a two-dimensional inviscid and incompressible flow when pushed out of dynamical equilibrium. We use the two-dimensional vorticity equation with spectral truncation on a rectangular domain. For a sufficiently large number of degrees of freedom, the equilibrium statistics of the flow can be described through a canonical ensemble 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 find numerical evidence that the distributions of the work performed satisfy the Crooks relation. We confirm our results by proving the Crooks relation for this system rigorously.
authors.affiliation: Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
authors.forename: Julia
authors.initials: J
authors.lastname: Gundermann
authors.affiliation: Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
authors.forename: Holger
authors.initials: H
authors.lastname: Kantz
authors.affiliation: School of Mathematical and Physical Sciences, University of Reading, Whiteknights, P.O. Box 220, Reading RG6 6AX, United Kingdom.
authors.forename: Jochen
authors.initials: J
authors.lastname: Bröcker