  Many complex and disordered systems fail to reach equilibrium after they have
been quenched or perturbed. Instead, they sluggishly relax toward equilibrium
at an ever-slowing, history-dependent rate, a process termed physical aging.
The microscopic processes underlying the dynamic slow-down during aging and the
reason for its similar occurrence in different systems remain poorly
understood. Here, we reveal the structural mechanism underlying logarithmic
aging in disordered mechanical systems, through experiments in crumpled sheets
and simulations of a disordered network of bi-stable elastic elements. We show
that under load, the system self-organizes to a metastable state poised on the
verge of an instability, where it can remain for long, but finite times. The
system's relaxation is intermittent, advancing via rapid sequences of
instabilities, grouped into self-similar, aging avalanches. Crucially, the
quiescent dwell times between avalanches grow in proportion to the system's
age, due to a slow increase of the lowest effective energy barrier, which leads
to logarithmic aging.
