Prigogine–Defay ratio for systems with more than one order parameter

The Prigogine–Defay ratio, Π≡ΔCp Δκ/TV (Δα)2, has been derived for systems whose states need to be specified in terms of a number of order parameters z by considering the conditions of tangency of the equilibrium free energy surface and the free energy surface for constant values of the order parameters. It is shown that Π?1. The equality applies for the case of a single order parameter or for the case of more than one order parameter which satisfies the constraint (∂V/∂zi)/ (∂S/∂zi) = (∂V/∂zk)/(∂S/∂zk). The inequality applies for the case of more than one order parameter which does not satisfy this constraint. The relevance of the Prigogine–Defay ratio to the kinetics of the structural relaxation in glass is discussed.