PlayStation 4 will be fully supported by Nvidia's PhysX middleware.
IGN reports Nvidia will release new PhysX and APEX software development kits which will include PlayStation 4 support.
Although you may only know the names from logos that flash by before you hit the title screen, PhysX and APEX are common and popular middleware tools for dynamic physics; they're responsible for destructible environments, ragdoll animations, fabric effects and much more. Loads of curent-generation games rely on it.
Although Nvidia would be a bit silly not to support the PlayStation 4 in this age of multiplatform development, it's still nice to get confirmation, since its rival AMD is supplying the guts of the machine.