I am going to send an email (including my CV) to a professor who has offered a postdoc position. Regarding recommendation letters or (any other contacts such as exchanging emails about me) between potential mentor of postdoc and my Ph.D. advisor, I would like to know that : Will the professor of postdoc send email to my adviser directly to ask a recommendation letter or any other questions about me without informing me?
Usually, one should not do this because it might have implication on your current position, especially if you are not selected afterwards.
Especially in academia, people might know each other very well and in such cases one might be tempted to make a short phone call or talk at a conference.
If you want to avoid this, you should explicitely mention, that you don't want that your current advisor will be contacted because [insert good reason here].