  de Sitter vacuum of nonconformal gauge theories is non-equilibrium,
manifested by a nonvanishing rate of the comoving entropy production at
asymptotically late times. This entropy production rate is related to the
entanglement entropy of the de Sitter vacuum of the theory. We use holographic
correspondence to compute vacuum entanglement entropy density $s_{ent}$ of mass
deformed ${\cal N}=4$ supersymmetric Yang-Mills theory - the ${\cal N}=2^*$
gauge theory - for various values of the masses and the coupling constant to
the background space-time curvature. For a particular choice of the curvature
coupling, the Euclidean model can be solved exactly using the supersymmetric
localization. We show that ${\cal N}=2^*$ de Sitter entanglement entropy is not
the thermodynamic entropy of the localization free energy at de Sitter
temperature. Neither it is related to the thermal entropy of de Sitter vacuum
of pair-produced particles.
