Abstract
We study the unitary time evolution of the entropy of entanglement of a one-dimensional
system between the degrees of freedom in an interval of length 
and its complement, starting from a pure state which is not an eigenstate of the
Hamiltonian. We use path integral methods of quantum field theory as well as explicit
computations for the transverse Ising spin chain. In both cases, there is a maximum speed
v
of propagation of signals. In general the entanglement entropy increases linearly with time
t
up to 
, after which it saturates at a value proportional to , the coefficient depending on the initial state. This behaviour may be understood as a
consequence of causality.