But how is this physically possible?
Some components, like Esaki diodes and glow tubes, have an I-V curve that is entirely in the I and III quadrants, but has a negative slope region over a limited range. In this region, a small-signal model of the device will have negative resistance.
In the Esaki diode, this behavior is caused by tunneling current that is possible at low bias but not at higher bias voltage.
It's also possible to make an op-amp circuit with negative input resistance over a limited range. There the I-V curve can even pass through the II and IV quadrants since power can be supplied from the op-amp's power terminals.
Somewhere I have read that an example of component with negative resistance is a voltage source.
Looking at the input side of a regulated switching supply with a fixed load, it will often appear as a negative resistance.
This is because it is a constant power load. If the input voltage drops, the regulator circuit will increase the current drawn in order to continue supplying the load with the desired output voltage.