2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160139In a recent paper Dajka, et.al., [J. Phys. A \textbf{40}, F879 (2007)] predicted that some composite systems can be entangled forever even if coupled with a thermal bath. We analyze the transient entanglement of a single-Cooper-pair box biased by a classical voltage and irradiated by a quantized field and find the unusual feature that the phase-damped cavity can lead to a long-lived entanglement. The results show an asymptotic value of the idempotency defect (concurrence) which embodies coherence loss (entanglement survival), independent of the interaction development by dependent critically on environment.15 pages, 4 figures, some modifications have been doneQuantum Physicstext