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Thermodynamical Property of Entanglement Entropy for Excited States and Holographic Local Quench

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In this talk, we will describe our recent
work.  Recently, we focus on the thermodynamical property and time
dependence of entanglement entropy. Using holography, we found that the
entanglement entropy for a very small subsystem obeys a property which is
analogous to the first law of thermodynamics when we excite the system. In
relativistic setups, its effective temperature is proportional to the inverse
of the subsystem size. This provides a universal relationship between the
energy and the amount of quantum information. Moreover, we will propose a new
holographic model of local quench and describe some results which we got by
using this model.

This talk is based on arXiv:1212.1164
[hep-th] and arXiv:1302.5703 [hep-th].