  Extending the analysis in our previous paper, we construct the entanglement
thermodynamics for a massless scalar field on the Schwarzschild spacetime.
Contrary to the flat case, the entanglement energy $E_{ent}$ turns out to be
proportional to area radius of the boundary if it is near the horizon. This
peculiar behavior of $E_{ent}$ can be understood by the red-shift effect caused
by the curved background. Combined with the behavior of the entanglement
entropy, this result yields, quite surprisingly, the entanglement
thermodynamics of the same structure as the black hole thermodynamics. On the
basis of these results, we discuss the relevance of the concept of entanglement
as the microscopic origin of the black hole thermodynamics.
