Exact anisotropic properties of hard spheres in narrow cylindrical confinement

We investigate a quasi-one-dimensional (Q1D) system of hard spheres confined within a cylindrical pore so narrow that only nearest-neighbor interactions occur. By mapping this Q1D system onto a one-dimensional polydisperse mixture of nonadditive hard rods, we obtain exact thermodynamic and structural properties, including the radial distribution function, which had remained elusive in previous studies. We derive analytical results for limiting cases, such as small pore diameters, virial expansions, and the high-pressure regime. In particular, we identify a crossover in the anisotropic pressure components: at high densities, the transverse pressure overtakes the longitudinal one when the pore diameter exceeds a critical threshold. We also examine spatial correlations in particle arrangements and radial fluctuations, shedding light on the emergence of ordering in confined systems.