Do you have a reference for "radian focusing". Quick Googling finds nothing. Focusing of CMB photons to a hot spot doesn't sound possible to me. If it is, then it must be possible to improve CMB detector sensitivity and I'm interested.

Looked into it and it's impossible, no optical system can increase surface brightness which is what defines temperature via it's intensity (flux per solid angle). In fact entropy and the 2nd law are locked into the optical engineering via the concept of "etendue" the product of area and solid angle.

Looks like the other two mechanisms are also compromised by basically the same reason. While there is an easy forward process (ratchet click or band-gap crossing) thermal fluctuations will provide the necessary kick in the opposite direction (freak backlash or thermal voltage jump) to exactly cancel the net flow

The dark current in circuits is proven by experiments and well published, but only taught to electrical engineers. They have to compensate for it with a small reverse potential to make reliable electronic devices. Much is written about how to minimize the dark current in components and circuits.

The ratchet has been argued long before it was possible to construct one. Opponents have assumed that a reverse potential would be allowed to accumulate sufficient to stop the ratchet or break it. The argument fails when the output movement is transmitted through a sufficiently low resistance.

I should have said Radiant Focusing ( not radian) under which title you should be able to find it published. Etendue is used in conservation of energy which is not the intent of my question. Anyone with a magnifying glass can increase the surface brightness of a spot on any object that is not a perfect reflector. A parabolic radio receiver antennae has increased the surface brightness of the target electrode.

When a prism separates ordinary light into colors the order of the output is greater than the input and no net work has been done on it. Entropy has decreased by addition of non random states to the system in the context of Schrödinger bringing order from chaos.

No you can't increase the surface brightness with a lens. If you focus the Sun into a spot you can only ever match it's 6000K surface brightness. The problem you can't focus into arbitrarily small spot because of the finite size of the Sun. You can try and go to a very fast lens with a short focal length to get a very small spot, but the the lens will have a small diameter, because of the small f-ratio (f-length/diameter) for a fast lens. Bigger diameter lens with have a longer focal length. the image will scale with the lens and so will have the same brightness. This is where the etendue comes in. The surface area times solid angle of rays from the Sun are conserved. Same problem with a parabolic radio dish.

In fact we did exactly what you suggested with the Planck satellite. A 1.5m mirror arrangement focused onto an array of horns (~5cm diameter @30GHz) and see still only see a 3K increase in the system temperature of the amplifiers not the (1.5/0.05)2 = 900 increase you suggest (ie 2700K!)

Interesting point about the prism and the spectrum, but I suspect the spreading out over the larger area increases the entropy in away compensates for the ordered spectrum. I should work it out.    

And I'm afraid "Radiant Focusing" doesn't give any useful information either.

Magnifying glass doesn't have to operate on the sun light, it can operate on any light source, even a cell phone. Then the lens can collect all the light and focus it to a bright spot smaller than the source. The etendue works in my favor.

Spreading out of the prism spectrum can be overcome by additional lenses that separate the colors and collect the rays into small beams of colored light. It's the unconventional view, and opinions are welcome.

Entropy is defined for random processes. Schrödinger has taken liberty with non random explanations of biology where the observed error rate of n replications is in parts per million, but the thermodynamic prediction is an error rate the square root of n.

Second law is defined for reversible processes. It doesn't say anything about a biased process  that doesn't reverse. The third law of thermodynamics can be represented in this way, instead of the abbreviated way it is presented to graduate students in college.

(S2 - S1) = R Ln (D2/D1)

This version of the third law governs all of the examples I have given if the view of Schrödinger is taken. Some important fundamentals are not taught in college, and are assumed to not exist. They can be found in old books by famous pioneers.  

I add one more example of light in a two way mirror. Energy is conserved, but entropy is altered by the glass.

Again the light from a birefringent crystal is separated and may be polarized. Entropy is altered by a passive object.

Rather than assert "the lens can collect all the light and focus it to a bright spot smaller than the source" give me an optical scheme where this is true. I think you will find the size of optical elements can't capture the all light to direct at the focus spot.

But the the prism is a reversible process. You can use another prism in reverse  to recombine the coloured rays back into a single white beam. In fact I think it was Newton who actually did this to prove the light wasn't being "pigmented" in any way. I think that says the entropy isn't changing.

I've thought about two way mirrors and that doesn't work either in the same way as materials with different reflectivities reach the same temperature. Consider a heat bath on one side of the mirror. Some light will leak through (say it's 99% reflective), but then it's trapped on the other side. Heat will build up until both side are at the same temperature and the leakage both ways is the same and equilibrium is reached.

Life is an open system, no equilibrium.

Thanks Ulla. This is the point I was trying to make. The conservation laws are well established, but sometimes applied where they are not defined.

The surprising thing to me is that science has largely accepted a spontaneous universe creation because of cosmic observations, but rejected all of the microscopic mechanisms that are offered to support such an event.

Schrödinger was obviously writing about a non reversible process, but until about 15 years ago much of science believed that the universe was reversible and would collapse to a final event even if dark matter was needed to accomplish it.

The question remains about how entropy was set so low in the beginning. It is easier to understand if the first event was not of random character and the irreversibility was established as a fundamental characteristic from the start.

Another possibility is that there occurred one and only one energy state that could be randomly filled at some point in the initial expansion.

S = k Ln (1)  which is zero.

It speaks of a saturation of energy in the small volume where all of the possible energy states are continually filled, expanding to a slightly larger volume in which one or a very few states can be randomly occupied.

My interest is in the concept of saturated energy density which may occur again as a limit to kinetic energy in deep space at high speed.