IS THERE A CANONICAL NONEQUILIBRIUM ENSEMBLE

We consider a simple dynamical system, related to the baker's transfor mation. This 'pastry-cook's transformation', operating in a space cons isting of two congruent squares, is performed by cutting both squares into q vertical slices, squashing each to 1/q of its previous height, rearranging the squashed slices to make two new squares as in the bake r's transformation, and finally interchanging the lowest p slices betw een the two squares. This transformation approximately mimics the ergo dic behaviour of a particle in a vessel consisting of two compartments separated by a diaphragm with a small hole in it occupying a fraction pig of the total surface area of either compartment. We show, for lar ge classes of initial ensembles and 'observable' dynamical variables, that the expectation value of any such dynamical variable at large tim es t is asymptotically the same as it would be in a 'canonical non-equ ilibrium ensemble' in which expectations are defined by E(g)[phi] = E (eq)[phi] + <h(x),g> <h(y),phi>. Here E(g) denotes an expectation tak en with respect to the initial phase-space density g, E(eq) denotes an expectation in the equilibrium ensemble, h(x), h(y) are certain linea r functionals, and phi = U-t f, where U is the evolution operator and f is an observable.