  We experimentally demonstrate how thermal properties in an non-equilibrium
quantum many- body system emerge locally, spread in space and time, and finally
lead to the globally relaxed state. In our experiment, we quench a
one-dimensional (1D) Bose gas by coherently splitting it into two parts. By
monitoring the phase coherence between the two parts we observe that the
thermal correlations of a prethermalized state emerge locally in their final
form and propagate through the system in a light-cone-like evolution. Our
results underline the close link between the propagation of correlations and
relaxation processes in quantum many-body systems.
