Double-well thermodynamic potentials and spinodal curves: how real are they?

The concept of double-well thermodynamic potentials, ubiquitous since the van der Waals description of the vapour-to-liquid transition and the Landau theory of phase transitions, is critically re-examined. Particular emphasis is put on the extent to which spinodal curves (separating ‘metastable’ from ‘unstable’ states) are meaningful. It is argued that in full thermodynamic equilibrium spinodals are well-defined when one either considers finite subsystems of an infinitely large system, or systems with all linear dimensions finite. Evidence is given that in a finite (cubic) d-dimensional box the spinodals correspond (in a fluid) to the rounded ‘droplet evaporation’ or ‘bubble condensation’ transitions, respectively, and are shifted inside the bulk coexistence region by amounts of order L − d / (d + 1), for a box of linear dimension L. The region in between the spinodals is the finite size analogue of the bulk two-phase coexistence region. Consequences for coarse-grained descriptions of the kinetics of phase transformations (e.g. cell dynamics simulations of spinodal decomposition, that start from a Ginzburg–Landau free energy functional) will be briefly discussed.