Here's an example:
http://orteil.dashnet.org/cookieclicker/Opening another tab creates a new bakery, not a view into the same bakery. (This only works if you haven't played before or clear your cookies.)
Edit:
If you really want to keep the same functionality then you would need to bring server communication into the mix. It's possible to either run the simulation server-side, or at least communicate the state between tabs using a server.
If you send an email in one Gmail window and it shows up in the other window, then I would guess it receives a message from the server to update.