  We present an elementary, general, and semi-quantitative description of
relaxation to gaussian and generalized Gibbs states in lattice models of
fermions or bosons with quadratic hamiltonians. Our arguments apply to
arbitrary initial states that satisfy a mild condition on clustering of
correlations. We also show that similar arguments can be used to understand
relaxation (or its absence) in systems with time-dependent quadratic
hamiltonians, and provide a semi-quantitative description of relaxation in
quadratic periodically driven (Floquet) systems.
