I'm game - let's do it
Great - yes 10 litre tanks.
If you insist on keeping air in the second tank, OK. If you can do it with a vacuum in there, the math is easier, but I'll do it your way.
Well, I was thinking real world and the empty tank has not been vacuum-pumped, so it does indeed have air in it, and yes, it will be ten litres and not one as I mistakenly wrote. Apologies for any confusion.
We have 10 liters of air at 200 bar and temp 273 K (0° Celsius) ....
no we do not... We have a ten litre cylinder at 200 bar which translates as 2000 litres of gas. And actually, I have done the calculations required (not math)... A cursory glance at my profile will indicate that I've been teaching this stuff for a while and have a little background in applied physics... which is actually about as useful as an ashtray on a motorcycle with this stuff, but whatever... Point is, I did the arithmetic.
I'm game - let's do it
I asked these questions:
1) Did it take energy to compress the gas into the donor tank?
2) Could we get some of that energy back by putting a pneumatic motor/generator in the whip line between the tanks and driving the generator by the pressure differential during the fill?
3) Would the recipient tank and donor tank equalize pressure regardless of whether we put a pneumatic motor/generator in the whip line?
4) What happens to the energy we could have extracted from the gas with the pneumatic motor/generator if we don't put the pneumatic motor/generator in the whip line?
Are they that hard?
1 and 2) Yes, this is then stored as the potential energy in the cylinder at 200 bar... lots of potential for that compressed gas to do work... we could run a haskel booster for example... but that would be energy inefficient... remember the three laws of thermodynamics: You can't win, you can't tie, and you can't get out of the game.
3) Yes, this process is called transfilling. Divers do it often. I had to do it last week. I used a transfill whip to transfer some diluent from a steel 16 litre cylinder to a steel 3 litre cylinder for my rebreather. (sidebar... a more useful and instructive topic and a little homework for you is this. The starting pressure in the 16 litre steel cylinder was 230 bar, while the three-litre was empty. When the pressure in the two had equalized, what was it, and how many litres of gas (in this case a 10/50 trimix) were left in the supply cylinder and how many in my diluent bottle? I am not interested in what the temperature shift was... but you are welcome to let us know.)
4) A portion of that potential energy is converted to heat. Some of that heat is dissipated through system components rather rapidly, some heats the gas that is compressed... and is then dissipated a little more slowly. Some remains in both tanks as potential energy. The net effect is that energy is neither created or destroyed... in keeping with the first law of thermodynamics and all that jazz... it is simply converted and spread around a little... wasted if you like.
This is all we need to know.
Your remaining "arguments" -- if I am reading them correctly -- seem to assume that energy can be created without any more work being added. It seems to me you are arguing a kind of perpetual motion machine.
Anyhow, I am done here.