  Linear response theory (LRT) is a key tool in investigating the quantum
matter, for quantum systems perturbed by a weak probe, it connects the dynamics
of experimental observable with the correlation function of unprobed
equilibrium states. Entanglement entropy(EE) is a measure of quantum
entanglement, it is a very important quantity of quantum physics and quantum
information science. While EE is not an observable, developing the LRT of it is
an interesting thing. In this work, we develop the LRT of von Neumann entropy
for an open quantum system. Moreover, we found that the linear response of von
Neumann entanglement entropy is determined by the linear response of an
observable. Using this observable, we define the Kubo formula and
susceptibility of EE, which have the same properties of its conventional
counterpart. Through using the LRT of EE, we further found that the linear
response of EE will be zero for maximally entangled or separable states, this
is a unique feature of entanglement dynamics. A numerical verification of our
analytical derivation is also given using XX spin chain model. The LRT of EE
provides a useful tool in investigating and understanding EE.
