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We derive the master equation that completely determines the time evolutionof the density matrix of the Unruh-DeWitt detector in an arbitrary backgroundgeometry. We apply the equation to reveal a nonequilibrium thermodynamiccharacter of de Sitter space. This generalizes an earlier study on thethermodynamic property of the Bunch-Davies vacuum that an Unruh-DeWitt detectorstaying in the Poincare patch and interacting with a scalar field in theBunch-Davies vacuum behaves as if it is in a thermal bath of finitetemperature. In this paper, instead of the Bunch-Davies vacuum, we consider aclass of initial states of scalar field, for which the detector behaves as ifit is in a medium that is not in thermodynamic equilibrium and that undergoes arelaxation to the equilibrium corresponding to the Bunch-Davies vacuum. We givea prescription for calculating the relaxation times of the nonequilibriumprocesses. We particularly show that, when the initial state of the scalarfield is the instantaneous ground state at a finite past, the relaxation timeis always given by a universal value of half the curvature radius of de Sitterspace. We expect that the relaxation time gives a nonequilibrium thermodynamicquantity intrinsic to de Sitter space.

Master equation for the Unruh-DeWitt detector and the universal relaxation time in de Sitter space