The rate of diffusive molecular motions, which are arrested at a glass tran
sition, is expected to depend on system size for sufficiently small systems
as a result of the cooperative nature of these motions. Two concrete pictu
res of such cooperativity are discussed: Sequences of coupled particle jump
s as occur in kinetically constrained lattice-gas models, and fluctuations
of collective flow as are apparent in MD simulations of simple liquids of h
igh density. Collective flow quantitatively explains the size dependence of
the velocity-autocorrelation functions (VAFs) at intermediate and long tim
es in a very dense binary liquid of hard spheres. A substantial size depend
ence of the VAFs is also found at short times t < 7 tau, where tau is the m
ean time of free flight, which so far is unexplained. The size dependence o
f the self-diffusion coefficients of the mixture depends sensitively on thi
s short-time behaviour.