  We consider two non-interacting infinite quantum spin chains immersed in a
common thermal environment and undergoing a local dissipative dynamics of
Lindblad type. We study the time evolution of collective mesoscopic quantum
spin fluctuations that, unlike macroscopic mean-field observables, retain a
quantum character in the thermodynamical limit. We show that the microscopic
dissipative dynamics is able to entangle these mesoscopic degrees of freedom,
through a purely mixing mechanism. Further, the behaviour of the dissipatively
generated quantum correlations between the two chains is studied as a function
of temperature and dissipation strength.
