  The dynamics of charge-ordered states is one of the key issues in underdoped
cuprate high-temperature superconductors, but static short-range charge-order
(CO) domains have been detected in almost all cuprates. We probe the dynamics
across the CO (and structural) transition in
La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_{4}$ by measuring nonequilibrium charge
transport, or resistance $R$ as the system responds to a change in temperature
and to an applied magnetic field. We find evidence for metastable states,
collective behavior, and criticality. The collective dynamics in the critical
regime indicates strong pinning by disorder. Surprisingly, nonequilibrium
effects, such as avalanches in $R$, are revealed only when the critical region
is approached from the charge-ordered phase. Our results on
La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_{4}$ provide the long-sought evidence for
the fluctuating order across the CO transition, and also set important
constraints on theories of dynamic stripes.
