Nanometer-scale pores in carbon-based materials such as graphene, carbon nanotubes, and two-dimensional polymers have emerged as a promising approach to high permeance, high selectivity gas separation membranes. In previous studies, quantum-mechanical mass-dependent tunneling, classical size-exclusion and differences in surface adsorption have been used to obtain high selectivity. Here, we illustrate a new classical approach in which an entropic barrier causes the selective separation of gas molecules. Using atomistic molecular dynamics simulations, we study the separation of ethane, ethene, propane, propene, n-butane, isobutane, 1-butene, cis-2-butene, trans-2-butene, isobutene, and 1,3-butadiene through a novel nanoporous two-dimensional hydrocarbon polymer (denoted PG-TP1), as a function of temperature and pressure. Despite the absence of a potential energy barrier for both types of species and the greater surface adsorption of the paraffins, selective passage of olefins results from the greater number...