Lieb-Robinson Bounds and Existence of the Thermodynamic Limit for a   Class of Irreversible Quantum Dynamics
  We prove Lieb-Robinson bounds and the existence of the thermodynamic limit for a general class of irreversible dynamics for quantum lattice systems with time-dependent generators that satisfy a suitable decay condition in space. 
Bruno Nachtergaele, Anna Vershynina, Valentin A. Zagrebnov
math-ph math.MP quant-ph