  We study the out-of-equilibrium evolution of a strongly interacting quantum
spin chain which is mapped on a system of hard rods that are coherently
deposited on and removed from a lattice. We show that this closed quantum
system approaches an equilibrium steady state which strongly resembles a
microcanonical ensemble of classical hard rods. Starting from the fully
coherent evolution equation we derive a Master equation for the evolution of
the number of hard rods on the lattice. This equation does not only capture
properties of the equilibrium state but also describes the dynamical
non-equilibrium evolution into it for the majority of initial conditions. We
analyze this in detail for hard rods of varying size.
