  In this work the TFD formalism is explored in order to study a dissipative
time-dependent thermal vacuum. This state is a consequence of a particular
interaction between two theories, which can be interpreted as two conformal
theories defined at the two asymptotic boundaries of an AdS black hole. The
initial state is prepared to be the equilibrium TFD thermal vacuum. The
interaction causes dissipation from the point of view of observers who measure
observables in one of the boundaries. We show that the vacuum evolves as an
entangled state at finite temperature and the dissipative dynamics is
controlled by the time-dependent entropy operator, defined in the
non-equilibrium TFD framework. We use lattice field theory techniques to
calculate the non-equilibrium thermodynamic entropy and the finite temperature
entanglement entropy. We show that both grow linearly with time.
