  We investigate the Joule expansion of nonintegrable quantum systems that
contain bosons or spinless fermions in one-dimensional lattices. A barrier
initially confines the particles to be in half of the system in a thermal state
described by the canonical ensemble and is removed at time $t = 0$. We
investigate the properties of the time-evolved density matrix, the diagonal
ensemble density matrix and the corresponding canonical ensemble density matrix
with an effective temperature determined by the total energy conservation using
exact diagonalization. The weights for the diagonal ensemble and the canonical
ensemble match well for high initial temperatures that correspond to negative
effective final temperatures after the expansion. At long times after the
barrier is removed, the time-evolved R\'enyi entropy of subsystems bigger than
half can equilibrate to the thermal entropy with exponentially small
fluctuations. The time-evolved reduced density matrix at long times can be
approximated by a thermal density matrix for small subsystems. Few-body
observables, like the momentum distribution function, can be approximated by a
thermal expectation of the canonical ensemble with strongly suppressed
fluctuations. The negative effective temperatures for finite systems go to
nonnegative temperatures in the thermodynamic limit for bosons, but is a true
thermodynamic effect for fermions, which is confirmed by finite temperature
density matrix renormalization group calculations. We propose the Joule
expansion as a way to dynamically create negative temperature states for
fermion systems with repulsive interactions.
