A Tesla diary is a collectible journal entry into Tesla's events leading up to the night of his death. These can be found throughout the mansion, from even his workshop on the second floor down to the secret basement. There are thirteen in total, so finding even one of these is enough to satisfy the trophy. If I remember correctly, there is one in the library as well as one in the sitting area outside Vandenberg's room on the second floor, so if you need one quickly, check either of these places.