General equations for the dependence of the thermodynamic driving force and the specific interfacial energy melt-crystal of critical clusters on temperature and pressure are derived. Analytical estimates of these and related thermodynamic quantities are advanced directly applicable in the analysis of experimental data of crystal nucleation. Similar to the well-known notation of a Kauzmann temperature, the concept of a Kauzmann pressure is introduced. It is shown that the thermodynamic driving force of crystal nucleation has a maxima not only at the Kauzmann temperature but also at the Kauzmann pressure. Estimates of the magnitude of the thermodynamic driving force of cyrstallization at these states are given and some consequences are discussed.