  We simulate dynamics of many-particle systems of bosons and fermions using
discrete time quantum walks on lattices. We present a computational proof of a
behavior of the simulated systems similar to the one observed in Hamiltonian
dynamics during quantum thermalization. We record the time evolution of the
entropy and the temperature of a specific particle configuration during the
entire dynamics and observe how they relax to a state we call quantum walks
thermal state. This observation is made on two types of lattices while
simulating different numbers of particles walking on two grid graphs with 25
vertices. In each case, we observe that the vertices counting statistics, the
temperature of the indexed configuration and the dimension of the effective
configuration Hilbert space relax simultaneously and remain relaxed for the
rest of the many-particle quantum walks.
