  Using ultrashort laser pulses, it has become possible to probe the dynamics
of long-range order in solids on microscopic timescales. In the conventional
description of symmetry-broken phases within time-dependent Ginzburg-Landau
theory, the order parameter evolves coherently, with small fluctuations along
an average trajectory. Recent experiments, however, indicate that some systems
can support a different scenario, named ultrafast inhomogeneous disordering,
where the average order parameter is no longer representative of the state on
the atomic scale. Here we theoretically show that ultrafast disordering can
occur in a minimal, yet paradigmatic, model for a Peierls instability if atomic
scale inhomogeneities of both the electronic structure and the charge density
wave order parameter are taken into account. The latter is achieved using a
non-equilibrium generalization of statistical dynamical mean-field theory,
coupled to stochastic differential equations for the order parameter.
