Thermodynamic curvature of a one-dimensional fluid

Abstract

We present investigations of the thermodynamic curvature in a one-dimensional hard-core square-well-potential continuum system of rods with a locus in the (T,P) plane across which the asymptotic decay of the correlation function crosses over from monotonic to oscillatory. For small temperatures, as the pressure is increased from zero, this system exhibits an abrupt pseudo-phase-transition from a gas-like phase of clusters of rods to a liquid-like phase. In the gas-like phase, where the correlation-function decay is monotonic, the thermodynamic curvature corresponding to the thermodynamics of the configuration integrals very nearly equals the correlation length for the long-range decay of the correlation function. In the liquid-like phase, where the correlation-function decay is oscillatory, the curvature is on the order of a rod length. These results are consistent with expectations based on a covariant thermodynamic fluctuation theory. During the pseudo-phase-transition, the curvature changes rapidly from gas-like to liquid-like behavior. During the rapid change, it overshoots to large negative values whose interpretation is yet unclear. Also yet unclear is the interpretation of the thermodynamic curvature based on the full thermodynamics, particularly at small pressures. In addition to examining the thermodynamic curvature, we reexamine the decay in the correlation function. We argue, on the basis of the amplitudes in the correlation-function series, that at small temperatures the crossover in the correlation-function decay from monotonic to oscillatory occurs effectively at the pseudo-phase-transition. This is consistent with the behavior of the thermodynamic curvature.