The living soul is what we call the Second Adam. It owns its vitality to the life-breath. There is no clear connection in the Bible, but it’s likely that the life-breath of the Old Testament (neshamah chay or ruwach chay) and the Sacred Spirit of the New Testament are identical. While the natural Adam only lived from the life-breath, Jesus was able to wield the Sacred Spirit to heal the sick and revive the dead. In this respect, Jesus appears as the perfection of Adam or mankind.
On a side note: Qabalah distinguishes between neshamah and ruwach. Ruwach is the life-power of Tiphareth and neshamah is the vital soul seated in Yesod. This distinction compares to the comparison of the ego and self we made in our post the Ego and Self.