•Energy variations of the liquid-solid transition in rapid and slow solidification.•A new thermodynamic interpretation of T0 curves based on energy analysis.•A “phase diagrams + T0 curves” indicator for exploring novel MGs and their GFRs. This study presents a new thermodynamic interpretation of T0 curves in eutectic phase diagrams. By analyzing the Gibbs energy variation of liquid-solid transition in energy-composition schematics, we illustrated the thermodynamic particularities of the T0 curves. They are experimentally observed to be boundaries between the partitionless crystallization and amorphous areas in phase diagrams. Our interpretation basically rationalizes the capability of T0 curves in predicting new glass forming systems and their glass forming regions. Good agreements between the thermodynamic indicator “phase diagram + T0 curves” for metallic glasses and the experimental information were obtained in typical systems.