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We consider two chains, each made of $N$ independent oscillators, immersed ina common thermal bath and study the dynamics of their mutual quantumcorrelations in the thermodynamic, large-$N$ limit. We show that dissipationand noise due to the presence of the external environment are able to generatecollective quantum correlations between the two chains at the mesoscopic level.The created collective quantum entanglement between the two many-body systemsturns out to be rather robust, surviving for asymptotically long times even fornon vanishing bath temperatures.

Long-lived mesoscopic entanglement between two damped infinite harmonic chains