Playstation 4 on a Thunderbolt display

The Apple press release says "supports DisplayPort for high resolution displays and works with existing adapters for HDMI, DVI and VGA displays", but this is referring to the Thunderbolt output port (for daisy-chaining). The Thunderbolt Display will not work with a non-Thunderbolt machine without an adapter.

But unfortunately now that the they have started shipping them, it has become clear that this does not apply to the input side of the display. As covered in the AnandTech review you can only connect Thunderbolt equipped computers into the Thunderbolt display.

That text in Apple's press release is oddly misleading. Because you also cannot connect a second DisplayPort to the Thunderbolt output socket on the display. You can however connect the Thunderbolt output to something like the Promise Pegasus then you can connect a DisplayPort display to the Pegasus. This seems to be a bug in the Thunderbolt Display, which will hopefully be fixed.

I expect someone could create an adapter that takes in HDMI/DVI, converts it to DisplayPort and outputs it as Thunderbolt. That should allow you to use the display with "legacy" formats, but such a thing does not yet exist and would no doubt be fairly expensive if it did.

There can be no such thing.

Thunderbolt is an active technology, Display Port is passive.
Adding the required circuitry to one end of such a cable would be pointless - it needs both ends to work.

Edit: Now I read your question again…

You have a Thunderbolt machine & a Display Port monitor…

That's Thunderbolt to Display Port not Display Port to Thunderbolt.

In which case DP to DP would be sufficient; the Thunderbolt circuitry would simply be inactive if you used Thunderbolt to Thunderbolt.
Display Port & mini-DP are the same thing, but different sizes.