Understanding the spreading of quantum correlations in out-of-equilibrium many-body systems is one of the major challenges in physics. For isolated systems, a hydrodynamic theory explains the origin and spreading of entanglement via the propagation of quasiparticle pairs. However, when systems interact with their surrounding much less has been established. Here we show that the quasiparticle picture remains valid for open quantum systems: While information is still spread by quasiparticles, the environment modifies their correlation and introduces incoherent and mixing effects. For free fermions with gain/loss dissipation we provide formulas fully describing incoherent and quasiparticle contributions in the spreading of entropy and mutual information. Importantly, the latter is not affected by entanglement of the system with the external environment. The mutual information is exponentially damped at short times and eventually vanishes signaling the onset of a classical limit. The behavior of the logarithmic negativity is similar and this scenario is common to other dissipations. For weak dissipation, the presence of quasiparticles underlies remarkable scaling behaviors.

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• Nonequilibrium & irreversible thermodynamics
• Nonequilibrium statistical mechanics
• Open quantum systems
• Quantum quench
• Nonequilibrium systems
• Quantum spin models
• Integrable systems