Thermodynamic States in Nonhomogeneous Systems: From Nanoscale to Macroscale

We analyze the mechanisms leading to thermodynamic stable states and isobaric phase transitions in finite nonhomogeneous nanosystems using classical molecular dynamics. We consider systems ranging from nano- to macroscopic scales and focus on spherical Lennard-Jones nanoparticles, in both one- and two-phase equilibria. In particular, we investigate how these systems' macroscopic behaviors evolve as their size increases. Our findings unveil that nonhomogeneous stable states are governed by spatial variations in intensive variables, contrary to standard thermodynamics of homogeneous systems, where equilibrium is described by extensive variables. Crucially, we demonstrate that nonhomogeneous intensive variables persistently diverge from homogeneous systems' predictions, even as the system size increases. Our calculations show that one-phase equilibrium is the direct consequence of the spatial variations of these intensive variables. In the two-phase equilibrium, such variations generate isobaric phase transitions across <i>finite</i> temperature intervals, through a continuous sequence that includes three-phase states. These temperature ranges <i>do not</i> vanish with increasing size, challenging the assumption that homogeneous systems are the asymptotic limit of finite nonhomogeneous systems. Our findings highlight the significance of boundary effects in understanding thermodynamic stability and equilibrium mechanisms, marking a departure from standard thermodynamic models that neglect these variations.