  Understanding relaxation processes is an important unsolved problem in many
areas of physics. A key challenge in studying such non-equilibrium dynamics is
the scarcity of experimental tools for characterizing their complex transient
states. We employ measurements of full quantum mechanical probability
distributions of matter-wave interference to study the relaxation dynamics of a
coherently split one-dimensional Bose gas and obtain unprecedented information
about the dynamical states of the system. Following an initial rapid evolution,
the full distributions reveal the approach towards a thermal-like steady state
characterized by an effective temperature that is independent from the initial
equilibrium temperature of the system before the splitting process. We
conjecture that this state can be described through a generalized Gibbs
ensemble and associate it with pre-thermalization.
