Simulating shear flow: Leave it to chance?

The phases of complex fluids at equilibrium are sufficiently diverse to keep physicists busy for the foreseeable future. The properties of such equilibrium systems are ultimately attributable to Boltzmann's law. When fluids are subjected to continuous shear flow, an equally rich spectrum of phase behaviours results, some of which I shall review. Yet we have no equivalent of Boltzmann's law to prescribe the statistics of these driven steady states. I shall discuss some tentative ideas concerning how a stochastic simulation might be constructed when Boltzmann is not at hand to guide us, and hope to instigate a debate on the validity of such a simulation.