Thermodynamic-like local atomistic entropy and enthalpy variables are introduced as a means to delineate and quantify phase transitions in atomistic simulations of extensional flow of an entangled polyethylene melt. These variables measure the local ordering and energetics at the monomer level, as opposed to the global system, and hence can be used to detect and quantify flow-enhanced nucleation events on small length and time scales that lead to flow-induced crystallization. The kinetics of the nucleating localized crystals can also be tracked using an atomistic Gibbs free energy composite variable. Based on the assumption that the global crystallization process followed a first-order reversible kinetic rate expression with a lag time, kinetic rate constants were calculated as functions of the Deborah number that allowed quantification of the flow-induced crystallization phenomenon exhibited by the simulated system under planar elongational flow at a temperature high above its quiescent melting point.