Limits of the equivalence of time and ensemble averages in shear flows
arXiv:cond-mat/0605633 · doi:10.1103/PhysRevLett.98.220602
Abstract
In equilibrium systems, time and ensemble averages of physical quantities are equivalent due to ergodic exploration of phase space. In driven systems, it is unknown if a similar equivalence of time and ensemble averages exists. We explore effective limits of such convergence in a sheared bubble raft using averages of the bubble velocities. In independent experiments, averaging over time leads to well converged velocity profiles. However, the time-averages from independent experiments result in distinct velocity averages. Ensemble averages are approximated by randomly selecting bubble velocities from independent experiments. Increasingly better approximations of ensemble averages converge toward a unique velocity profile. Therefore, the experiments establish that in practical realizations of non-equilibrium systems, temporal averaging and ensemble averaging can yield convergent (stationary) but distinct distributions.
accepted to PRL - final figure revisions