Entropy-driven phase separation and configurational correlations on a lattice: Some rigorous results

We prove that if there is a phase separation in a fully packed (FP) athermal system, it must be between pure components only. We then rigorously demonstrate that no phase separation in an athermal FP state of hard particle mixtures on a lattice is possible merely due to size disparity or nonadditivity, if the configurations are weakly correlated, i.e., are quasirandom. We consider a mixture of linear polymers at all packing fractions and argue that no phase separation is possible in an athermal state. The last result also applies to a mixture of flexible particles and hard dimers. Our results contradict many recent numerical results.