  We observe that in presence of excitation, a thermodynamic Smarr like
relation corresponding to a generalized entanglement temperature ($T_g$) can be
holographically obtained for the entanglement entropy of a subsystem. Such a
relation emerges naturally by demanding that the generalized entanglement
temperature produces the exact Hawking temperature as the leading term in the
IR limit ($l\rightarrow \infty$). Remarkably, this relation has the same form
as the Smarr relation in black hole thermodynamics. We demonstrate this for
three spacetime geometries, namely, a background with a nonconformal factor, a
hyperscaling violating geometry background, and a charged black hole background
which corresponds to a field theory with a finite chemical potential.
