Composition fluctuations in polydisperse liquids: Glasslike effects well above the glass transition

We study a two-dimensional glass-forming system of slightly polydisperse (LJ) particles using molecular dynamics simulations and demonstrate that in the liquid regime (well above the vitrification temperature) this model shows a number of features typical of the glass transition: (i) the relation between compressibility and structure factor $S(q)$ is strongly violated; (ii) the dynamical structure factor $S(q,t)$ at low $q$ shows a two-step relaxation; (iii) the time-dependent heat capacity ${c}_{v}(t)$ shows a long-time power-law tail. We show that these phenomena can be rationalized with the idea of composition fluctuations and provide a quantitative theory for the effects (i) and (ii). It implies that such effects must be inherent in all polydisperse colloidal models, including binary LJ mixtures.