
We study the low-temperature limit of bosonic continuous-variable systems under Markovian thermal environments, with the goal of making precise when entanglement can becomethe operationally dominant resource shaping experimentally accessible correlations.The main technical result is an exact entanglement threshold for symmetric two-modesqueezed thermal states (TMST), expressed in closed form through the PPT/symplecticeigenvalue criterion. This provides a controlled benchmark: for fixed squeezing strength,cooling alone can drive a preparation from separable to entangled below a critical temperature.Building on this benchmark, we propose an entanglement-dominant regime definedby a timescale inequality between entanglement generation and effective decoherence,and we outline how this criterion can be mapped to platform-level parameters (damping,dephasing floors, and thermal occupancies).Extensions to collective modes and multipartite settings are presented as an outlookand as a numerical/experimental program, emphasizing what is rigorously proven versuswhat is to be tested.
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