title: Thermodynamical property of entanglement entropy for excited states.
abstract: We argue 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. We derive the results using holography and confirm them in two-dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy.
authors.affiliation: Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8582, Japan.
authors.forename: Jyotirmoy
authors.initials: J
authors.lastname: Bhattacharya
authors.forename: Masahiro
authors.initials: M
authors.lastname: Nozaki
authors.forename: Tadashi
authors.initials: T
authors.lastname: Takayanagi
authors.forename: Tomonori
authors.initials: T
authors.lastname: Ugajin