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.

在这项工作中，为了研究耗散时间相关的热真空，探索了 TFD 形式。这种状态是两种理论之间特定相互作用的结果，可以将其解释为在 AdS 黑洞的两个渐近边界处定义的两个共形理论。初始状态准备为平衡 TFD 热真空。从在边界之一测量可观察量的观察者的角度来看，相互作用会导致耗散。我们表明，真空在有限温度下演变为纠缠态，耗散动力学由非平衡 TFD 框架中定义的瞬态熵算子控制。我们使用晶格场理论技术来计算非平衡热力学熵和有限温度纠缠熵。