  We study nonequilibrium dynamics of relativistic $N$-component scalar field
theories in Minkowski space-time in a classical-statistical regime, where
typical occupation numbers of modes are much larger than unity. In this
strongly correlated system far from equilibrium, the role of different
phenomena such as nonlinear wave propagation and defect dynamics remains to be
clarified. We employ persistent homology to infer topological features of the
nonequilibrium many-body system for different numbers of field components $N$
via a hierarchy of cubical complexes. Specifically, we show that the persistent
homology of local energy density fluctuations can give rise to signatures of
self-similar scaling associated with topological defects, distinct from the
scaling behaviour of nonlinear wave modes. This contributes to the systematic
understanding of the role of topological defects for far-from-equilibrium time
evolutions of nonlinear many-body systems.
