If a physical system is perturbed from equilibrium, the rate that it equilibrates is an important measure of its physics. In condensed matter physics, we are used to measuring such rates in the context of linear response to electromagnetic fields. For instance, the rate that current decays in a metal after an electric field impulse can be related to the width of its low-frequency “Drude” response in the optical conductivity. The rate that polarization decays after polling a liquid with an E field corresponds to the width of the broad peak in the Debye relaxational functional form. In contrast, the rate of energy relaxation is a fundamental rate that governs many processes in solids, but which is unfortunately not measured straightforwardly via conventional electrodynamic linear response. However quite generically, this rate can be measured in various non-linear chi3 spectroscopies. I will discuss recent technical developments in the form of THz range 2D coherent spectroscopy (and its relatives) that allow us to get new information about energy relaxation in correlated and topological metals, as well as disordered electron glasses. I will discuss a number of systems and phenomena in which unconventional dynamics and energy relaxation govern their low energy behavior. I will give number of examples of the power of these new techniques to strongly interacting metals, Dirac semimetals, collective modes in superconductors, electron glasses, and 1D spin chains.

[1] Fahad Mahmood et al., "Observation of a marginal Fermi glass”, Nature Physics 2021
[2] D. Barbalas et al., https://arxiv.org/abs/2312.13502
[3] K. Katsumi https://arxiv.org/abs/2311.16449 to appear in PRL 2024
[4] R. Bhandia, https://arxiv.org/abs/2405.03002