The influence of long-range chain connectivity on the thermodynamic properties of athermal compressible single component and binary polymer mixtures is studied for the lattice model both theoretically and by Monte Carlo simulations. Theoretical expressions for the thermodynamic properties are derived based on the chain insertion probabilities. The chain conformations enter the theoretical insertion probabilities by the number of intramolecular contacts. The distribution of the number of intramolecular contacts of a single athermal chain is taken as input, of which the dependence on density is predicted by the theory. The theory successfully predicts the Monte Carlo simulation data for the equation of state of pure components and mixtures. Also microscopic details on the different types of self-contacts and cross contacts in the mixtures are accurately predicted.