Entanglement entropy and Fisher information metric for closed bosonic strings in homogeneous plane wave background

We derive the extended renormalized entanglement entropy and the Fisher information metric in the case of closed bosonic strings in a homogeneous plane wave background. Our investigations are conducted within the framework of thermo field dynamics. The formalism is also illustrated in the example of some particular models in condensed matter physics and the nonequilibrium case for a system with dissipations.