Yes everything besides hot gas all the time has T=0.
They will appear photons, but they will vanish asymptotically.
With time the temperature of gas reduces also asymptotically to 0, so it's entropy is reduced.
So after infinite time photons vanishes - we have only gas between separators with T=0 and two mirrors with kinetic energy - the entropy of this system achieved minimum - is smaller than initial by entropy of heat of initial gas.
Entropy should change continuously, so there exists finite time for which entropy would be already smaller.
In other words we've changed the energy stored in heat of the gas into ordered kinetic energy of mirrors, which can be easily changed into work.
For such idealized models we can assume that mirrors are perfect separators for photons - doesn't absorb heat, but thanks of momentum conservation they absorb some momentum and so energy as kinetic energy.
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If You don't like idealized unpractical models, there are also two very practical: one for us and one for organisms which lives hundreds of meters below and have extremely weak access to chemical energy, but they have plenty of energy around in heat (and tectonic vibrations...).
http://groups.google.com.my/group/sci.bio.evolution/browse_thread/thread/4813249d0945f637
Both of them uses microscopic mechanisms.
Usually released microscopic energy quickly escape and change into heat.
We can use that sometimes these releases are spatially localized, so local 'mechanisms' can help to put this energy into more stable form like potential energy of electron in a circuit or chemical energy of some molecule (like ATP).
The first example uses that thermal infrared can not only be emitted/absorbed by single molecules, usually using their vibrational/rotational energy, but also for example by a free electron in a circuit - by nanoantenna.
The energy of this electron when it absorbs photon is relatively huge - it's highly improbable that it gain this energy thanks of thermal energy only and emit a photon - absorption will dominate here.
The problem is to rectify this electricity, but we can use that it is highly localized.
This electron will naturally equilibrate its energy with environment, but this process is relatively slow, require some length of way through circuit.
So the nearer electron is to the antenna, the higher average energy it statistically have.
The whole electricity generator could look like (parallel):
-conductor-threshold-antenna-conductor-threshold-
and electrons should more likely go left, because after absorbing a photon, they equilibrate their energy while going through conductor.
If the antennas are printed as in the work of prof. Novack I've linked, required threshold could be just narrowing/ gap.
Before going to the second example, let's think about crystallization.
It obviously increases ordering (reduce entropy), but total entropy doesn't decrease because the binding energy (difference between energy of the molecule in solution (larger) and after binding (smaller) ) is stored in unstable form of energy (kinetic/vibration/rotation energy) that quickly equilibrate its energy with environment, increasing heat/entropy.
But what if this binding energy would be stored in stable form, like chemical energy (ATP)/conformation ? Such energy stored in ATP can be used in order way to create work (for example using myosin).
Remember that joining to growing 'crystal' is localized reaction - could use help of an enzyme as catalyst, which additionally stores part of binding energy in stable form like in ATP.
The second example uses just two molecules instead of whole crystal.
Let say that we have two molecules(A,B) which has larger total energy
separated(E1) than when they are bind (E2
Additionally there is energy barrier between these states (as usual).
Now when they are bind in solution, their thermal energy statistically
sometimes exceed the barrier and they split, taking require energy from heat -reducing temperature!
But to bind them back, they not only have to reach the barrier, but
they have also to find each other in the solution - it's not very
likely, so statistically concentration of AB is relatively small
comparing to concentration of separated molecules.
Now we will need a catalyst which reduce the barrier, but then use the
energy difference for example to bind ADP and phosphate.
For example it catches all required molecules and uses just gained energy or energy stored in own structure to take A and B closer, to make them reach the top of the barrier, then use energy they produce to bind ADP + P and restore own energy.I know - this enzyme would work in both directions, but concentration
of AB should be relatively small, it doesn't have to use whole binding energy, such that the wanted direction should dominate.
Organisms can enforce required optimal concentrations.
Returning to thermodynamics - it's derived averaging local behaviors.
It's kind of mean field approximation - forgets about correlations ... which can give very different behaviors/interactions ... like different stability of stored energy.
I agree that it can pass simplified models or tests like Maxwell's demon, but it's far from being proved to be universal property.
Remember that 2nd law is not required to forbid machine which creates work for infinity, conservation of energy/momentum already forbids it.
2nd law forbids only ordering energy stored in chaotic thermal movement.
But if this law isn't always true, there would be other counter intuitive implications, like that computation could need no energy...
But remember that quantum computation would theoretically also offer it - computation is invertible - doesn't use energy. Energy is requiredonly to read result.
