Quantum thermodynamics of holographic quenches and bounds on entanglement growth from QNEC
ABSTRACT :
The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a subregion along a null direction. Motivated by recent studies of quantum thermodynamics, we study if the QNEC restricts quenches in holographic many-body systems. We find that an increase in entropy and temperature is necessary but not sufficient to not violate QNEC in quenches that lead to transitions between BTZ geometries dual to thermal states carrying angular momentum. For an arbitrary initial thermal state, we can determine the lower and upper bounds on the temperature (entropy) increase that is necessary for a fixed increase in entropy (temperature) in order to satisfy the QNEC. Our study shows that the entanglement entropy thermalizes in time l/2 where l is the length of the entangling region with an exponent 3/2 for an arbitrary allowed transition generalizing earlier results. Furthermore we are able to determine the rate of initial quadratic growth exactly for any transition as a function of l and show that the QNEC bounds it. We also show that for a semi-infinite region the slope of the ballistic growth of entanglement at late time is simply twice the difference of the entropy densities of the final and initial states in consistency with the eigenstate thermalization hypothesis. We show that our methods can shed light on the validity of Landauer erasure principle, the design of quantum engines and more generally on the applicability of quantum resource theories in holographic many-body systems. This talk is based on upcoming papers in collaboration with Avik Banerjee, Nehal Mittal, Ayan Mukhopadhyay and Pratik Roy.