# Maximum-energy records in glassy energy landscapes

## TL;DR

This paper investigates how the maximum energy reached over time evolves in models with glassy landscapes, providing insights into aging dynamics and identifying threshold energies through numerical simulations.

## Contribution

It offers a detailed theoretical description of the evolution of maximum energy in glassy systems and demonstrates how this can identify threshold energies in $p$-spin glasses.

## Key findings

- Evolution of $E_ ext{max}(t)$ described from short times to equilibrium.
- Maximum energy records can identify threshold energy in $p$-spin models.
- Comparison with simulations validates theoretical predictions.

## Abstract

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 energy landscapes, in instant quenches from infinite temperature to a target temperature $T$. Through a detailed description of the activated dynamics, we are able to describe the evolution of $E_\max(t)$ from short times, through the aging regime, until after equilibrium is reached, thus providing a detailed description of the long-time dynamics. Finally, we compare our findings with numerical simulations of the $p$-spin glass and show how the maximum energy record can be used to identify the threshold energy in this model.