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.
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