Of course I mean we should add a generator for sim to go OU. This generator is the negative resistor. However, I see a problem in our thinking. You seems to say the input to the negative resistor is the same as negative resistor output. If so, there is no OU. I also do not see what's the point of negative resistor in this.
I don't see where is the problem. It is the same thing with a generator. OU is just a mind view of an inexhaustible extra-energy source. If it is coming from a neg resistance or from a perpetual voltage generator, it doesn't change anything since the moment you include it in a sim.
So I don't understand what you mean. A negative resistance is a dipole where current and voltage variations are proportional but of opposite directions (one increases when the other decreases). In real neg resistances, this applies only in a voltage and current range around a particular point of polarisation. The required energy to produce the effect is provided by the polarization source. Outside of the range, the dipole becomes non linear and loses its property of negative resistance.
In an ideal neg resistance, the effect doesn't depend on a biasing voltage point, it is available for all currents and voltages, including variations around V=0.
We can see real neg resistances where a limited variation of voltage/current around a functioning point is concerned, or ideal ones, as following:
The reverse sign of the power due to the reverse sign of the current compared to the voltage, indicates that the energy is provided or consumed. The relative direction of current and voltage in a neg resistance shows that it acts as a generator.
Now, what is OU? "OU" is only an idea of the consequence of an inexhaustible source of energy that we could tap. There are two ways to see it, depending on what type of "perpetual motion" we invoke. If we speak of type 1, then OU in a closed system is extra-energy coming from nothing. It is likely that none of us think it is possible. We preferably refer to perpetual motion of type 2. In this frame, OU is extra-energy due to an unknown source and coming from outside of our (apparently) closed system into it, proving that our system was not really closed.
A sim can't show OU:
- a sim follows the equations of academic science, implying energy conservation in a closed system. A sim can't guess nor detect that there would be a source of extra-energy adding up in the system if it is not talked that there is one.
- and if we include the extra-energy source, then this source becomes conventional from the viewpoint of the simulation, and so the sim will not show OU, the energy is still conserved because our system includes now the energy source, so it is really closed.
When we include a neg resistance in a sim, the signal in the sim can diverge but there is still an energy balance between production and consumption. It is the same thing when we connect a (positive) resistance to a voltage generator in a sim: the energy becomes infinite with time, but this doesn't prove OU.
Only the inextinguishable character of the energy source can prove "OU": this is always presumed in a sim when using a generator or a neg resistance, therefore OU can be shown and proved only ouside the frame of a simulation.