Here are two quotes from Bruce McCormack on Barth’s theology of eternity, history, and being; and then how that all impacts concepts like impassibility and immutability. These are not uncontroversial. The first quote would be controversial among Barth scholars who take a more “textual” reading of Barth (like Hunsinger and Molnar), while the latter quote would be controversial among trad Protestant theologians who affirm a classical understanding of immutability and impassibility as it comes to a theology proper. What do you think?
For Barth, Jesus Christ is his history. He is the history set in motion by an eternal act of self-determination; hence, the history that he is finds its root in election. This is what he is “essentially.” Jesus Christ is what he is in his eternal act of self-determination and in its outworking in time. The implications for a putative divine timelessness should be clear: Already in Church Dogmatics, II/1, Barth had treated “eternity” as something that is defined by God’s being. The concept is used illegitimately where it is filled with content drawn from some other quarter and then applied to God. Moreover, Barth had already claimed that eternity is that which founds time, that which provides time with its basis. And it would be hard to see how it could be anything else. If God’s eternal act of self-determination is a determination for existence as a human being in time, then it is the eternal decision itself which founds time. And if God’s being is, on the basis of this decision, a being-for-time, then clearly God’s being cannot be timeless. We would do better to understand the decision in eternity and its outworking in time to be a single activity, one which originates in eternity and is completed in time. But this then also means that time is not alien to the innermost being of God.
The critique of impassiblity requires a further step. Who, we might well ask, is the Subject who suffers in Jesus of Nazareth? We have just seen how a commitment to impassibility [prior discussion to these two quotes] led to an understanding of the Logos as an absolute metaphyscial Subject, with the consequence that it became necessary to treat the human nature as a Subject in its own right, capable of a suffering which had no ontological implications for the Logos. That such a conception tilts in the direction of Nestorianism is clear. What Barth has done, however, is to insist that a single-Subject Christology such as Chalcedon’s cannot make this move. There can be only one Subject of the human sufferings of Jesus, and this Subject is the Logos. That the Logos suffers humanly goes without saying. Suffering is made possible only through the assumptio carnis. But it is the Logos who suffers, for there is no other Subject. Even more important where the concept of impassiblity is concerned, Barth has also closed the gap between the Logos and his divine nature. If the Logos is the Subject of the human sufferings of Jesus, then suffering is an event which takes place within the divine life—which also means that the divine “nature” cannot be rightly defined in abstraction from this event. The divine nature can rightly be defined only by this event. The net consequence of this move is that Barth is able to advance an understanding of divine immutability which is no longer controlled by the further thought of impassiblity. If becoming human, suffering and dying, and so forth, are the content of the eternal decision in which God gives himself his being, then no change is introduced into the being of God when this becoming and so forth take place in time. And if God is immutably determined for suffering, then the concept of immutability has been cut loose from impassibility.
 Bruce L. McCormack, ed.,Engaging the Doctrine of God: Contemporary Protestant Perspectives, 222.
 Ibid., 222-23 [brackets mine].