  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.
