This is an extended version of my Nobel Lecture, delivered on December 8, 2021. I will
recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe …

Memory and rejuvenation effects in the magnetic response of off-equilibrium spin glasses
have been widely regarded as the doorway into the experimental exploration of …

The Mpemba effect occurs when a hot system cools faster than an initially colder one, when
both are refrigerated in the same thermal reservoir. Using the custom-built supercomputer …

The understanding of the dynamics of nonequilibrium cooling and heating processes at the
nanoscale is still an open problem. These processes can follow surprising relaxation paths …

The study of spin-glass dynamics, long considered the paradigmatic complex system, has
reached important milestones. The availability of high-quality single crystals has allowed the …

Cooling and heating faster a system is a crucial problem in science, technology, and
industry. Indeed, choosing the best thermal protocol to reach a desired temperature or …

Spin glasses (SGs) are paradigmatic models for physical, computer science, biological, and
social systems. The problem of studying the dynamics for SG models is nondetermistic …

The correlation length ξ, a key quantity in glassy dynamics, can now be precisely measured
for spin glasses both in experiments and in simulations. However, known analysis methods …

Experiments featuring non-equilibrium glassy dynamics under temperature changes still
await interpretation. There is a widespread feeling that temperature chaos (an extreme …

We review the main methods used to study spin glasses. In the first part, we focus on
methods for fully connected models and systems defined on a tree, such as the replica …