MarkT:
Not even laser action? Travelling wave tube? Seems pretty close to the definition as in both cases the
signal is being added to as it goes through...
Well a laser is not increasing the energy each photon caries, that is fixed by it's frequency. What the laser does is add more photons of the same energy to the stream.
So, philosophically does a transistor amplify a current the same way? Yes. A few (well, a lot, but on the grander scale ...) electrons cause the flow of more electrons due to the way they interact with quantum transitions in the atoms of the 'amplifying medium'. Lasers do that with photons, transistors can do that with electrons.
I used italics above because as pwillard says above, "Nearly all the examples we deal with here in Arduino-land reside in the digital realm where the transistors "active amplification mode" is mostly irrelevant because we are using it in "saturation" mode". That's true for me. I use transistors as kind of a relay. It's either on or off.