Note on entanglement temperature for low thermal excited states in higher derivative gravity

We investigate the entanglement temperature of a small scale subsystem in low excited states by using holographic method. Especially, we study the entanglement entropy and entanglement temperature in higher derivative gravities which are considered as low thermal excitation of pure AdS gravity. We find that the entanglement entropy are related to the central charges of CFT living on the boundary. The relation between the variance of entanglement entropy and energy of a small scale subsystem has been also obtained. Furthermore, the relation is consistent with the first law-like relation that is proposed by Phys. Rev. Lett. 110 (2013) 091602. Finally, we derive the formula of the variance of entanglement entropy in general excited states in gravity background with the Fefferman-Graham coordinates and the entanglement temperature can be figured out in special case.