  We study the temporal evolution of the circuit complexity for a subsystem in
harmonic lattices after a global quantum quench of the mass parameter, choosing
the initial reduced density matrix as the reference state. Upper and lower
bounds are derived for the temporal evolution of the complexity for the entire
system. The subsystem complexity is evaluated by employing the Fisher
information geometry for the covariance matrices. We discuss numerical results
for the temporal evolutions of the subsystem complexity for a block of
consecutive sites in harmonic chains with either periodic or Dirichlet boundary
conditions, comparing them with the temporal evolutions of the entanglement
entropy. For infinite harmonic chains, the asymptotic value of the subsystem
complexity is studied through the generalised Gibbs ensemble.
