  We analyze fermions after an interaction quantum quench in one spatial
dimension and study the growth of the steady state entanglement entropy density
under either a spatial mode or particle bipartition. For integrable lattice
models, we find excellent agreement between the increase of spatial and
particle entanglement entropy, and for chaotic models, an examination of two
further neighbor interaction strengths suggests similar correspondence. This
result highlights the generality of the dynamical conversion of entanglement to
thermodynamic entropy under time evolution that underlies our current framework
of quantum statistical mechanics.
