If I've been to Turkey once and enter at a later point with the same travel document, when my travel document is scanned at the border, do my previous entries and exits pop up on their screen?
If it matters, how does it work at land borders?
It appears that Turkey has an effective entry/exit tracking system where this information is available. This Wikileaks cable from the US Embassy (unclassified) indicates as such (this one provides additional information):
-- What computerized immigration databases are used to track entries and exits? See REF B. A COMPUTERIZED IMMIGRATION DATABASE IS COLLECTED AND MAINTAINED BY THE TURKISH NATIONAL POLICE (TNP) FOREIGNERS' POLICE.
-- Is the computerized immigration database available at all ports of entry (POEs)? YES.
-- How often are national immigration databases updated? DAILY. NOTE: THE TNP USED TO HOLD EXIT-ENTRY RECORDS ONLY FOR THE PREVIOUS TEN YEARS. RECORDS ARE NOW KEPT INDEFINITELY, ALTHOUGH POST BELIEVES TNP BEGAN KEEPING RECORDS ONLY IN THE EARLY 1990S. ALSO, BOTH TURKISH CITIZENS AND FOREIGN TRAVELERS MAY NOW OPT NOT/NOT TO HAVE THEIR PASSPORTS STAMPED WITH ENTRY AND EXIT STAMPS. NONETHELESS, AN ELECTRONIC RECORD IS KEPT OF THE EXIT OR ENTRY.
-- What are the country's policies (legislation, mandates, etc.) on collecting information from travelers arriving in the country? IT IS MANDATORY FOR THE TNP TO COLLECT EXIT AND ENTRY INFORMATION ON ALL TRAVELERS. (THE SOLE EXCEPTION IS THE POPE.)
-- Are there different policies for entry and exit at air, sea, and land POEs and for domestic flights? NO.
-- If immigration databases are available at some POEs, but not all, how does the host government decide which POEs will receive the tool? All POEs collect data. Data on visitors is also collected by hotel staff when visitors check into hotels in Turkey.
This doesn't conclusively prove that the information is immediately available on their screens or if they have to take some action to get it, but it is clearly collected and available to the police for immigration purposes.