Metastability and the Kramers Escape Rate

Here is a double well, U of x equals x squared minus one, squared, drawn as the purple curve on the back wall. Its two minima, at minus one and plus one, are separated by a barrier of height one.

On the floor, time runs away from us. Each blue path is a particle following Langevin dynamics at temperature one quarter. A path rattles inside one well for a long time, and only now and then hops across the barrier.

The rest of the narration is in the book's Companion.