Time dependent Entanglement Entropy in dissipative conformal theories: TFD approach

TL;DR

This paper employs the TFD formalism to analyze the evolution of entanglement entropy in dissipative, time-dependent conformal theories, revealing linear growth of entropy due to dissipation in a non-equilibrium setting.

Contribution

It introduces a novel application of TFD to study dissipative dynamics and entanglement entropy in conformal theories at finite temperature.

Findings

Entanglement entropy grows linearly with time.

Dissipative dynamics are governed by a time-dependent entropy operator.

Non-equilibrium thermodynamic entropy also increases linearly.

Abstract

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.