  We derive a formula for the entanglement entropy of squeezed states on a
lattice in terms of the complex structure J. The analysis involves the
identification of squeezed states with group-theoretical coherent states of the
symplectic group and the relation between the coset Sp(2N,R)/Isot(J_0) and the
space of complex structures. We present two applications of the new formula:
(i) we derive the area law for the ground state of a scalar field on a generic
lattice in the limit of small speed of sound, (ii) we compute the rate of
growth of the entanglement entropy in the presence of an instability and show
that it is bounded from above by the Kolmogorov-Sinai rate.
