The Prigogine-Defay ratio and the microscopic theory of supercooled liquids

Prigogine-Defay ratios and, more recently, their frequency extension have been proposed to be a measure of the number of nonmacroscopic processes involved in the relaxation dynamics of supercooled liquids. We show that the microscopic theory of the Navier-Stokes equations of those liquids provides a consistent thermodynamic framework in which all possible dynamical Prigogine-Defay ratios can be expressed in terms of the same relaxation functions and that these ratios provide less information than the microscopic theory itself. The latter shows that more than one relaxation process is certainly always involved in this relaxation dynamics, whatever is the molecular dynamics, or experimental, technique used to determine the latter.