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 energy-momentum tensor in terms of the variation of the entanglement entropy of a sub-region along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, are necessary but not sufficient to not violate QNEC in quenches leading to transitions between thermal states with momentum which are dual to Banados-Teitelboim-Zanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of entropy (temperature) for a fixed increase in temperature (entropy). Our results provide explicit instances of quantum lower and upper bounds on irreversible entropy production whose existence has been established in literature. We also find monotonic behavior of the non-saturation of the QNEC with time after a quench, and analytically determine their asymptotic values. Our study shows that the entanglement entropy of an interval of length $l$ always thermalizes in time $l/2$ with an exponent $3/2$. Furthermore, we determine the coefficient of initial quadratic growth of entanglement analytically for any $l$, and show that the slope of the asymptotic ballistic growth of entanglement for a semi-infinite interval is twice the difference of the entropy densities of the final and initial states. We determine explicit upper and lower bounds on these rates of growth of entanglement.

5+6 pages, 2+5 figures; version to appear in PRL

References in corpus (11)

• Irreversible entropy production, from quantum to classical
• Thermalization of Strongly Coupled Field Theories
• "Light-cone" dynamics after quantum quenches in spin chains
• Generalized Clausius inequality for nonequilibrium quantum processes
• Irreversible work and inner friction in quantum thermodynamic processes
• A holographic view on physics out of equilibrium
• Relative Entropy of Random States and Black Holes
• Quantum Null Energy Condition and its (non)saturation in 2d CFTs
• Distinguishing Random and Black Hole Microstates
• The inside outs of AdS(3)/CFT(2): Exact AdS wormholes with entangled CFT duals
• A Renyi Quantum Null Energy Condition: Proof for Free Field Theories

Cited by in corpus (11)

• Holographic spacetime, black holes and quantum error correcting codes: A review
• Erasure tolerant quantum memory and the quantum null energy condition in holographic systems
• Proof of Renyi QNEC for free fermions
• Nambu-Goto equation from three-dimensional gravity
• Black hole complementarity from microstate models: A study of information replication and the encoding in the black hole interior
• How Gubser flow ends in a holographic conformal theory
• Generalized Clausius inequalities and entanglement production in holographic two-dimensional CFTs
• Holographic Gubser flow: A combined analytic and numerical study
• Quantum null energy condition in quenched 2d CFTs
• The degrees of freedom of multiway junctions in three dimensional gravity
• Local Geometric Bounds on Generalized Entropy Evolution along Null Horizons