I just wonder since money has to enter the system somehow. Currently the Fed will supply whatever banks ask to meet their capital needs. But how much physical currency does the Fed, treasury, and mint transfer to banks per year? And which banks?
The amount of currency in circulation (bills and coins) is published by the Federal Reserve. (Available at the FRED web site.) The annual change in this time series is the amount created.
This is the amount outstanding, it does not tell us how much currency is being destroyed and replaced. Also, there is seasonal demand for currency, and some cash is shipped back and forth.
The creation of currency is not really a "transfer" (gift). The banks need to buy the currency by exchanging reserves (settlement balance at the Fed) for the notes.
Finally, the Federal Reserve does not single out how much it deals with any particular banks by name under normal circumstances. (During some of the special operations undertaken after the Financial Crisis, the Fed published some information about their counterparties.) The most you would get would be on the basis of the category of bank.
In the US and in the Eurozone, a lot of the money doesn't physically exist - this graph illustrates it quite nicely. In Europe, only 1,1B of the 10B Euro in circulation are cash (source) - all the remainder is electronic. When banks need money from the Fed, there is an electronic transaction from the Fed to the bank.
Cash is introduced in the economy through banks, through their request to the central bank for cash, provided upon need and perhaps against a fee.
The specific amount is irrelevant because it is just a gift to banks.
The currency "purchases" are offset by deducting their account, which is based on fractional reserves, which are limited by a reserve ratio based on how much currency the bank has. Which is a circular logic, and thus meaningless. Banks can withdraw whatever they feel like from the Fed.
Economics is of course about pretending that banks are bounded by some kind of law or whatever