To apply to Entropy you shove a living snake up your ass, or write a dissertation on cake and the little-known goddess SHODAN. After that, you're supposed to doppel WANTED people and masquerade as them, using your conjurer clairvoyance ability to tell the Vindicator where you are. You also can retrieve your cabal item only whenever the fuck you need Doppel or chromatic flame or randomize or displacement.
...okay so I never did that, but it would have made Pico laugh.
...I miss Entropy.