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We study the evolution of the maximum energy $E_\max(t)$ reached between time$0$ and time $t$ in the dynamics of simple models with glassy energylandscapes, in instant quenches from infinite temperature to a targettemperature $T$. Through a detailed description of the activated dynamics, weare able to describe the evolution of $E_\max(t)$ from short times, through theaging regime, until after equilibrium is reached, thus providing a detaileddescription of the long-time dynamics. Finally, we compare our findings withnumerical simulations of the $p$-spin glass and show how the maximum energyrecord can be used to identify the threshold energy in this model.

Maximum-energy records in glassy energy landscapes