Thermodynamic States in Non homogeneous Systems:From Nanoscale to Macroscale

We analyse the mechanisms leading to thermodynamic stable states and isobaric phase transitions in finite non-homogeneous 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 non-homogeneous 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 non-homogeneous 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 finite temperature intervals, through a continuous sequence that includes three-phase states. These temperature ranges do not vanish with increasing size, challenging the assumption that homogeneous systems are the asymptotic limit of finite non-homogeneous 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.