eyeinthesky has it spot on. Yup, 500fpm is the minimum without informing atc, but the word expedite means nothing. I don't believe it is mentioned in any AIP (feel free to correct me there) but even if it is, it opens up such a huge grey area that it cannot be used for separation purposes. As mentioned above, expedite for an A340 EDDF-KLAX means something totally different than it does for a B737-800 EDDL-EGLL.
Its simple for me, if you need a specific ROC/D in order to achieve separation, that ROC/D needs to be specified in the clearance, and read back by the pilot. Even then, depending on the situation, (opposite direction traffic for example) another solution must be kept on standby.
The use of "expedite" is, IMHO usually a result of the controller having missed a conflict when issuing a climb or descent clearance. I know, I've done it myself, and had my wrist slapped by my supervisor.