Quantum thermodynamics of holographic quenches and bounds on the growth of entanglement from the QNEC
Abstract
The quantum null energy condition (QNEC) is a lower bound on the energymomentum tensor in terms of the variation of the entanglement entropy of a subregion along a null direction. To gain insights into quantum thermodynamics of manybody systems, we study if the QNEC restricts quenches driven by energymomentum inflow from an infinite memoryless bath in twodimensional holographic theories. We find that an increase in both entropy and temperature are necessary but not sufficient to not violate QNEC in quenches leading to transitions between rotating thermal states described by BanadosTeitelboimZanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of temperature (entropy) that is necessary for a fixed increase in entropy (temperature). We also establish monotonic behavior of the nonsaturation of the QNEC with time for allowed final states and analytically determine their asymptotic values  these should have new implications for the null shape variation of the relative entropy of the quenched state. Our study shows that the entanglement entropy always thermalizes in time $l/2$, where $l$ is the length of the entangling region, with an exponent $3/2$. Furthermore, we are able to determine the rate of initial quadratic growth of entanglement analytically in terms of thermodynamic data for any $l$, and show that the QNEC bounds it from above and below. We also show that the slope of the asymptotic ballistic growth of entanglement for a semiinfinite interval is simply twice the difference of the entropy densities of the final and initial states.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.09914
 Bibcode:
 2021arXiv210909914K
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 5+5 pages, 6 figures