The transfer of entanglement and Bell-nonlocality from system to environment

The entanglement among three cavities is transferred to three reservoirs. So does the Bell-nonlocality. Sudden death of entanglement among the three cavities could occur before, simultaneously with, or after sudden birth of entanglement among the three reservoirs. However, sudden death of Bell-nonlocality among the three cavities always happens before sudden birth of Bell-nonlocality among the three reservoirs. The survival time of entanglement is much longer than that of the Bell inequality violation.