Thermodynamic constraints and pseudotransition behavior in a one-dimensional water-like system

Abstract: We investigate a one-dimensional water-like lattice model with Van der Waals and hydrogen-bond interactions, allowing for particle number fluctuations through a chemical potential. The model, defined on a chain with periodic boundary conditions, exhibits three ground-state phases: gas, bonded liquid, and dense liquid, separated by sharp phase boundaries in the chemical potential and temperature plane. Using the transfer matrix method, we derive exact analytical results within the grand-canonical ensemble and examine the finite-temperature behavior. The system exhibits clear pseudotransition features, including sharp but analytic changes in entropy, density, and internal energy, along with finite peaks in specific heat and correlation length. To assess the role of thermodynamic constraints, we consider the behavior under fixed density through a Legendre transformation. This constrained analysis reveals smoother anomalies, such as entropy kinks and finite jumps in specific heat, contrasting with the sharper grand-canonical signatures. These results underscore the ensemble dependence of pseudotransitions and show how statistical constraints modulate critical-like behavior. We also verify that the residual entropy continuity criterion holds in the grand-canonical ensemble but is violated when the system is constrained. Our findings illustrate how even a simple one-dimensional model can mimic water-like thermodynamic anomalies.