Abrupt transitions in physics and biophysics: van der Waals revisited.

An iteration procedure that relates pressure and volume changes in the condensation of a gas by means of two independent relations of the volume and the effective pressure predicts abrupt volume transitions similar to those experimentally observed. Similar abrupt transitions are predicted for a molecular association in which the association free energy is dependent upon the extent of reaction. The pressure, or the concentration, at which the abrupt transition occurs depends upon the volume, or the extent of reaction, used to initiate the iteration procedure and selection of the transition that corresponds to the equilibrium requires additional conditions. For the gas condensation, assumption of the symmetry of the effects of the pressure fluctuations at equilibrium gives results that coincide with those obtained by application of the Maxwell rule. From these observations it is concluded that abrupt transitions arise naturally when independent conditions cannot be simultaneously satisfied.