  In this thesis we study properties of open quantum dissipative evolutions of
spin systems on lattices described by Lindblad generators, in a particular
regime that we denote rapid mixing. We consider dissipative evolutions with a
unique fixed point, and which compress the whole space of input states into
increasingly small neighborhoods of the fixed point. The time scale at which
this compression takes place, or in other words the time we have to wait for
any input state to become almost indistinguishable from the fixed point, is
called the mixing time of the process. Rapid mixing is a condition on the
scaling of this mixing time with the system size: if it is logarithmic, then we
have rapid mixing.
  The main contribution of this thesis is to show that rapid mixing has
profound implications for the corresponding system: it is stable against
external perturbations and its fixed point satisfies an area law for mutual
information.
