Entanglement Rates and the Stability of the Area Law for the   Entanglement Entropy
  We prove a conjecture by Bravyi on an upper bound on entanglement rates of local Hamiltonians. We then use this bound to prove the stability of the area law for the entanglement entropy of quantum spin systems under adiabatic and quasi-adiabatic evolutions. 
Micha\"el Mari\"en, Koenraad M.R. Audenaert, Karel Van Acoleyen, Frank   Verstraete
math-ph math.MP quant-ph