How to simulate adjustable 'negative resistance' with active components?
That positive passive resistance you have in your box is very 'pure'. Low noise, wide bandwidth, very low reactive components (depending on construction), floating with respect to ground, and very robust against transient high voltages and currents, without clipping or croaking.

You can rig up an opamp or two, with power followers, that can force the current pulled and pushed into/out of a pair of nodes to be proportional to a scale factor of their differential voltage, and that scale factor can be positive or negative, and controllable by a pot.

However, that circuit will have limited bandwidth, add noise, will have stray impedances to ground, and will clip for small overloads and will die with large overloads, depending on how conservatively you design it. 

Were I to try such a thing, my biggest problem would be deciding on a specification. I'd start off with a capacity of 1v and 1amp, then think again and it would grow to until it was too large to build. 

What can you do with good low Rdson FETs for switches, you could manage mOhms? But it will still be non-zero, and positive.