Nonequilibrium size distributions of fluid membrane vesicles

We investigate nonequilibrium behavior of polydisperse ensembles of fluid membrane vesicles by means of a diffusive Boltzmann transport equation that incorporates vesicle diffusion and reactions between vesicles. This approach is used to study time evolutions of size distributions of initially monodisperse vesicle ensembles. We investigate various nonequilibrium paths that ensembles of vesicles may follow during the equilibration process. Depending on the initial size distribution of vesicles, the thermodynamic equilibrium may be reached either via a fusional growth of vesicles, or via their fissional decay. In the former case, typical vesicle size grows as R(t)similar to t(1/2) Until it saturates to its equilibrium value, whereas in the latter case we find that vesicle size decays in a finite time proportional to [R(0)](1/3), where R(0) is the initial vesicle size. The latter behavior is related to the length scale dependence of membrane bending and saddle splay rigidity.