Electromagnetic or microwave cooling

One way to think of a inductor from the circuit's point of view is that it gives inertia to current. This gives you some intuitive feel for why current builds up slowly as voltage is applied, and why the voltage goes as high as it needs to on a attempt to shut off the current abruptly. This isn't how the physics works, but this can be a very useful mental model for understanding and designing circuits with inductors.

The passive terminations \$Γ_g\$ and \$Γ_l\$ must be added so that the input and output resonate at the same frequency of oscillation. For this purpose, the 2 and 3 conditions are used. In other words, if the oscillator is oscillating at one port then it has to oscillate at the other port too.

there's a proof too for two port oscillator design. Suppose oscillation condition is met at port 1 then from second condition,

\$ \dfrac{1}{Γ_{in}}=Γ_g \$

Now we know, \$Γ_{in} = s_{11} + \dfrac{s_{12} \cdot s_{21} \cdot Γ_l} {1-(s_{22} \cdot Γ_l)} \$

substituting Γin formula in the equation, we can easily get, \$ \dfrac{1}{Γ_{out}}=Γ_l\$.

And hence if one port is oscillating then the other port has to oscillate simultaneously. And thats what condition 2 and 3 convey.