Comment Re:Passive propulsion (Score 1) 322
Why does the second law say no to arbitrarily concentrating energy?
Because it lets me extract useful work simply from a hot environment with no cold reservoir. I just put my box in a room and it gradually gets hotter while the room gets colder. After a while I set up a heat engine between them and extract some work from the difference. Then I can repeat the process: this time, the room can't heat the box as well, but the room is colder too, so the heat engine still works. Eventually I can get (almost -- see the 3rd law) all the heat from the room extracted as useful work, which is not allowed.
(By "arbitrarily" I meant "without reason or effort" rather than merely "without bound". Sorry for any confusion.)
Surely the fact that you are drawing all your energy from outside the system (your box) would allow for a localised loss of entropy, given the gains in entropy outside the system.
Entropy goes the other way: any normal physical system that gets hotter gains entropy, so the box would be gaining it and the room losing it. But hot systems (by definition!) gain less entropy from, say, a joule of heat than cold systems do. This is the reason for the unidirectional flow of heat: if I'm hotter than you, you lose more entropy giving up a joule than I gain from getting it, so we can't send the heat that way.