Information dynamics of different quantum systems under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multilevel atoms and the effects arising from the coupling to the reservoir. Even in the presence of the reservoirs, the inherent entanglement is found to be rather robust. Due to this fact, together with control of system parameters, the system may therefore be especially suited for quantum information processing. Information entropy, entropy squeezing and wehrl entropy are discussed as indicators of entanglement. Our findings also shed light on the evolution of open quantum many-body systems.


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