Maxwell's Demon Goes Electric?

Anybody who took some physics in HS and has a little imagination can understand how Maxwell's Demon thought experiment works.

So far it has been understood though the experiment is only evocative or allegorical as it can not work in reality.

You have two rooms full of gas molecules with a door in the middle, small enough for only one molecule to pass at the time. If you possess a demon (a small enough intelligent being) that has the capacity to open the small door and the energy used to open and close that door would be negligible and the demon would be smart enough to open the door each time when a fast molecule comes from right and close it when a fast one comes from left, after a while you would have all the slow molecules in the right room and all the fast ones in the left. And of course that difference of temperature could create energy if using something like a Stirling motor. But you could also commandeer the demon to open the door for all molecules coming from right or left and after a while you would have vacuum in one room and pressure in the other which again you could use to power something.

I think i've identified a couple of instances when this is happening in nature or within existing technology. Let's say you have a similar room filled with a gas with a layer of liquid of the same substance at the bottom (separated by gravity), at a pressure both phases can coexist. Due to thermal agitation there will be a continuous exchange of molecules between gas and liquid phases. However, molecules move much faster in gas phase than liquid. Because of that the molecules escape the liquid at a slower speed than some (of the fastest) gas molecules enter back the same liquid. Also, as soon as the slower raising (evaporating) molecules get hit by faster ones in the gas phase, they should enter back the liquid again at lower speeds than fastest moving in upper layer of gas and so on. So you would have a small strata at the surface of the liquid where gas will have a lower temperature that the rest.

No matter how much i've searched, i could not find anything clear and simple about such a commonly seen phenomena, the speed of electrons moving in a metal. Main reason is, you guessed, nobody ever saw them moving. Everybody agrees the electrons inside a metal are in a cloud like state, with electrons moving freely around. But as for the speed, there are many differences of opinions, because of the different models they use. In classical physics, that can explain some of the phenomena, they are moving at speeds comparable to speed of light. In quantum, you guessed, they are waveforms and the speeds can't be known exactly. However they all agree about the drift speed, the speed at which the electric charges of electrons move together when an external electric field is applied, creating what they call an "electric current" but that speed is excruciatingly slow, for practical currents, (where conductors will be stable or won't heat up and vaporise) the speeds are in the order of mm/sec. From that and from calculations it results that only a very small fraction of moving electrons or better said only a small fraction or the axial component of the speed of electrons makes our practical current.

However much more is known about the flow of currents in pure (intrinsic) semiconductors. When an electric field is applied, electrons jump from one atom to another, leaving behind "holes" that in turn are creating again electric fields (on top of the externally applied field) that are attracting other electrons in a cascading effect. This way, the average speed of electrons jumping around is always limited, if not constant at a few discrete values (have to consider acceleration and deceleration between two jumps or the paths of electrons). I found a GIF that illustrates this phenomenon.

The more interesting part happens however whey you put two of these together, on the left a pure metal and at right next to it a pure semiconductor like in series and attach a battery on the sides (your electric field) in such a way (polarity) that electrons will flow from the metal into the semiconductor. Electrons cannot enter the semiconductor at the speeds they float around in metal but only at drifting speed.

Though some models say electrons move around at speeds comparable to speed of light, in all directions, if a bunch of those would hit the semiconductor they will vaporise it, hower that is not happening. What is happening though and we can measure it, is an electric current (same) is flowing through both and the speed of that current is "regulated" by the jump speed of electrons in semiconductor.

We all know that any current generated by an external field that translates into drifting (axial motion) of the electrons through a metal generates heat. Some models predict drifting current represent a very small fraction of the motion of electrons. However if the electrons were moving in the metal at high speed, they will be slowed down by collisions with the lattice and all their energy will be turned into heat.

Though, ultimately heat itself keep the electrons moving. Compared to materials that don't have free electrons, at the same temperature the lattice itself will agitate less because some of the heat will be carried by (free moving) electrons. As i just read on a site, metal is part solid with a gas or liquid (of electrons) flowing through it, which explains thermal conductivity and other phenomena.

(By this simple idea i think we can actually calculate the non-drifting average speed of the electrons at different temperatures, by rule of three or something close including the lattice vibration, starting with the temperature difference and drift speed generated by a current that we can calculate. Which shouldn't be that high. Actually comparable with the drift speed).

By continuing this line of reasoning. At a metal/semiconductor junction with flowing of current from metal to semiconductor, electrons from the metal will be caught in newly created "holes" within the semiconductor due to external field but also due to field created by the hole itself. But within certain limits, of various speeds and directions, since the speed and generally motion of electrons in metal is random due to collisions with its own lattice. Some of them will have axial speeds exceeding the capacity of the semiconductor lattice to retain them (both external and hole field) and will be rejected back in the metal though at a lower speeds (some momentum of the electron will be transferred throughout the lattice, creating agitation or heat), where they will collide again with metal's lattice again and eventually some will come back at lower speed and be retained after a number of cycles and finally start jumping, in the direction of the field, maybe a bit more at first, but not enough to overheat the lattice (we know how keep the current below that limit, from previous trials), with again some momentum (heat) transferred between them and semiconductor lattice, until all they all reach "regular" jumping speed. So here again we come to the conclusion that electrons are being selected by the junction in a way similar to molecules in Maxwell's experiment, though in both "rooms" particles (electrons) are constantly moving (flowing) to the right though in metal they are moving more, because they are moving in all directions and carry some of the total thermal energy of the metal. So from a cloud of electrons moving randomly through the metal lattice at thermal agitation speed and drifting speed in the electrical field we extract in the semiconductor only those moving at drifting speed and we can all agree that the drifting speed is lower than the average speed of electrons moving in the metal lattice.

Some would call these phenomena that occur all around us "rectifying" the brownian motion (of molecules or electrons) and it has been admitted by mainstream that if this would be possible, it would be a source of unlimited energy. That's where our intelligence must intervene and  harvest the free energy that exist all around us. (If only we wouldn't be so busy with plotting and be slaves to fake theories).

Would the universe collapse or fragment or shatter into multiverses if we start doing that? I don't think so cause heat pumps do this for decades and nothing happened so far (that we know about, or maybe the Universe is not expanding so much anymore).

Got you thinking, maybe a little?