It is common for professors to have cordial relationships with their colleagues who work in different institutions (obviously), and I was wondering if it is also common for them to exchange info about their PhD applicants during the application review season. For example, if a promising candidate has applied to the chemistry programs at University X and University Y, would the people in the admissions committees of these two chemistry programs potentially contact each other to discuss the prospects of this student?
People might discuss the pool of applicants generally—what percent is international, what was the admit rate, etc.—but never an individual candidate's application.
The only time I could imagine an admission committee member discussing a candidate's application is if someone on the committee (or in the department, if it's more decentralized) knows one of the people who wrote the candidate's letters of reference and wants to get more direct information than what's written in the letter.
This would be a breach of privacy, so this normally does not and should not happen. What would be the advantage anyway? Even if professors have close collaboration, each professor wants the best candidate. Of course if you directly contacted a couple of professors from different institutions then they might discuss students interested in their lab, but usually only if you are a really good prospect - but this would not be in relation to your admission.