PhysX is in no way limited to only Nvidia cards, but only Nvidia have the hardware built in to handle the calculations for it. If no PhysX compliant hardware is detected, the load will be passed on to the CPU. Advanced PhysX, on the other hand is exclusive to Nvidia and cannot be used with AMD cards without massive lag, as it is highly unoptimized for CPUs.
Borderlands 2 is a little bit different in that it doesn't really use advanced PhysX at all but rather allows you to set the level of PhysX effects between Low, Medium and High. Obviously it will run better on an Nvidia system, but a beefy CPU can also handle Borderlands 2 PhysX at the Medium setting.