  We study the holographic supersymmetric Yang-Mills (SYM) theory, which is
living in a hyperbolic space, in terms of the entanglement entropy. The theory
contains a parameter ($C$) corresponding to the excitation of the SYM theory,
and it controls the dynamical properties of the theory. The entanglement
temperature ($T_{ent}$) is obtained by imposing the thermodynamic law for the
relative entanglement entropy and the energy density of the excitation. This
temperature is available at any value of the parameter $C$ even in the region
where the Hawking temperature disappears. With this new temperature, the
dynamical properties of the excited SYM theory are examined in terms of the
thermodynamic law. We could find the signatures of phase transitions of the
theory.
