Relaxation dynamics in thermal and athermal systems

We study deterministic and stochastic gradient descents in random energies $E_\varepsilon(x) = V(x) + \varepsilon W(x/\varepsilon)$; $V$ is the deterministic part of the energy, $W$ is a realization of the energy fluctations and $\varepsilon$ is the typical distance between local minimal of $E$.

If the evolution of $x$ for given $\varepsilon$ and $W$ is deterministic one obtains classical rate independent evolution in the limit where $\varepsilon$ tends to 0. We extend the analysis to the stochastic case and find a generalization of rate-independent evolution which exhibits a nontrivial relaxation dynamics. Our results can potentially explain well-known creep phenomena such as Andrade creep in plasticity.

This is joint work with Michael Ortiz (Caltech), Marisol Koslowski (Purdue) and Tim Sullivan (Caltech).