  Thermalization in closed quantum systems can be explained either by means of
the eigenstate thermalization hypothesis or the concept of canonical
typicality. Both concepts are based on quantum mechanical formalism such as
spectral properties of the eigenstates or entanglement between subsystems
respectively. Here we study the onset of thermalization of Bose particles in a
two-band double well potential using the truncated Wigner approximation. This
allows us to use the familiar classical formalism to explain quantum
thermalization in this system. In particular, we demonstrate that sampling of
an initial quantum state plays the role of a statistical mechanical ensemble,
while subsequent chaotic classical evolution turns the initial quantum state
into the thermal state.
