Brownian motion

Classically, yes.
But in qm, there is no such thing as 0 kinetic energy. That would violate heisenberg uncertainty principle.

Not true either.

Complementary variables position AND momentum cannot be known at any given time due to the principle. This however means that you can measure the momentum as 0 and be uncertain of its position and it still has no kinetic energy.

If my assumptions are incorrect you can fill me in with the reasons why, but I'm quite sure this is the case.

How come can't heat be turned into work? Isn't it being turned into work when the particles move?

You disagree with me but your argument supports my claim.

Read the wiki on absolute zero. They also state kinetic energy is non zero in the ground state of a particle.

Another example is the infinite potential well. Even when all possible energy is removed from the particle, it still has non zero energy. It can still be found in different places in the box. So it has kinetic energy.

>No.
That's not entirely the whole picture. There is such a thing as brownian engines, it's just that they can't extract work from a single temperature environment, they do extract work from a difference in temperature like any engine, but the mechanism they use is brownian motion.

>This however means that you can measure the momentum as 0 and be uncertain of its position
No, you would need to have a particle diffracted over all of space to know its momentum is 0. Since you're likely working within boundaries, there is a lower bound on the momentum.

Please read en.wikipedia.org/wiki/Maxwell's_demon
with emphasis on Richard Feynman's analysis.

If we agree (as I think we do) that useful energy cannot be extracted without exploiting a temperature difference, then there is no need to "replenish" anything. So, with regard to original query "This is probably somehow related to atomic energy?", the answer is firmly "No!"

>There are proofs of this
except they arent. It cant even be tried. Temperature itself has no reson to generate movement. Diference in tempreatures, on the other hand...

how come it cant be extracted?? I mean, the particles are moving as a river move... Just that I still had not any solid answer. "Just heat" does not produce movement if there are not changes or fluctuations. If it did, we should be able to create energy out of a constant temperature, wich violates maxwellls principle. So how do they move, again? How is the work of moving the particles done infinitely without temperature fluctutions? Why are molecules suposed to bounce anyways?

A full explanation is too long to post here. (Hey, if Fermat could use that excuse, so can I) but I refer you to Feynman's analysis summarized at en.wikipedia.org/wiki/Brownian_ratchet

"The Character of Physical Law" goes through the logic, step by step, in detail.

that is bullshit, later ill tell you why, gotta go

This.

The problem is compounded if you're measuring a crystal at low temperature because then the lattice defines inherent boundaries to the particles in the system. There is then a non-zero KE at 0 K.

>"particles have kinetic energy at absolute 0"
>what is the definition of absolute 0 guise, i dont know tee hee

Ok i am back, there is no reason why all the mechanism of the brownian motor should be sumerged inside the water, so this explanation

youtu.be/LqVeBxtZbj0?t=11m33s

is wrong.

>"a state at which the enthalpy and entropy of a cooled ideal gas reaches its minimum value, taken as 0"
>minimum value
>minimum possible KE, not zero KE