This paper presents simulations of the physical aging of a binary Kob-Andersen-type Lennard-Jones liquid following large temperature up jumps from equilibrated states of high relaxation time. The purpose is to investigate how well the Tool-Narayanaswamy (TN) material-time concept works for this rather extreme case of aging. First, the triangular relation of the potential energy is investigated. This is found to be well obeyed, making it possible to define a potential-energy-based material time $\xi$. We proceed to study aging toward equilibrium at the final temperature 0.48 for jumps from the two temperatures 0.43 and 0.37 (primarily), monitoring the following five quantities: the potential energy, the self-intermediate scattering function, the mean-square displacement, the dynamic susceptibility ${\chi }_4$, and the non-Gaussian parameter ${\alpha }_2$. The TN material-time prediction is that all time-autocorrelation functions should collapse to only depend on the material-time difference ${\xi }_2-{\xi }_1$. This is found to work better for the $0.43\to 0.48$ temperature jump than for the $0.37\to 0.48$ jump. Our findings thus confirm the general understanding that the TN aging formalism works best for systems that are never very far from equilibrium. This raises two questions for future work: Is the collapse significantly improved if each aging quantity is allowed its own material time? Can better collapse be obtained if the material time is generalized to be locally defined (in order to reflect dynamic heterogeneity)?

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• Molecular dynamics