STATISTICAL-MECHANICS OF FLUIDS UNDER INTERNAL CONSTRAINTS - RIGOROUSRESULTS FOR THE ONE-DIMENSIONAL HARD ROD FLUID

The rigorous statistical mechanics of metastability requires the impos ition of internal constraints that prevent access to regions of phase space corresponding to inhomogeneous states. We derive exactly the Hel mholtz energy and equation of state of the one-dimensional hard rod fl uid under the influence of an internal constraint that places an upper bound on the distance between nearest-neighbor rods. This type of con straint is relevant to the suppression of boiling in a superheated liq uid. We determine the effects of this constraint upon the thermophysic al properties and internal structure of the hard rod fluid. By adding an infinitely weak and infinitely long-ranged attractive potential to the hard core, the fluid exhibits a first-order vapor-liquid transitio n. We determine exactly the equation of state of the one-dimensional s uperheated liquid and show that it exhibits metastable phase equilibri um. We also derive statistical mechanical relations for the equation o f state of a fluid under the action of arbitrary constraints, and show the connection. between the statistical mechanics of constrained and unconstrained ensembles.