Picture 2This correspondence can be seen easily if the diagram is rotated such that the axes are exchanged, as shown.
And this is the result.
Picture 3This is the result of the above operation. I have taken the same image as in picture 1 and rotated it; I left the subscripts out of the operation in order to leave them more readable.
Compare this to the original diagram in the temperature article:
Picture 1The image shows how internal energy changes upon increase of entropy; if this suggests to you that it must be possible to take control of the entropy of a system, then you are on the right path. Keep in mind that the changes in the system we are discussing here are caused by the addition of heat, and this, by definition, is the transfer of energy while changing entropy. Thus, by heating or cooling (among other), you can control the entropy of a system.