Trying to tell a warmer what the Boltzmann equation does say and what it does not say is like trying to educate an outback bushman that the tribe`s witch doctor does not have supernatural powers.
The only thing this equation: σT1^4 - σT2^4 states is the amount of work (as in energy) can be transfered from a mass A at T1 to another mass B at T2.
If T1>T2 then energy is transfered from A to B, but never the other way around.
The warmers insist it is reversible enabling B to transfer energy to A because there are photons coming from A that B absorbs.
There are, nobody says there are not.
But that does not TRANSFER ENERGY from B to A, because in order to do that B has to increase the ENERGY of A, which means
work was performed on the mass A with ENERGY being consumed that came from B. If that were possible then A should now be able to perform more work than it could before that backward process happened.
Warmers are unable to realize how absurd their interpretation of the Boltzmann equation is, reject any proof of the contrary and if all fails they invoke a third body C that finally explains why A can perform more work because B was there.
All the while there is proof that only A to B transfer can happen and not B to A. It`s everywhere you look and can observe a thermodynamic process that performs work.
Expanding the liquid in a bulb thermometer requires work, as does the expansion of a gas.
If you put some hot liquid A in a thermos and screw the top on the hot liquid will heat the colder air B that makes up the head space in that thermos.
You can observe that by connecting a manometer tube to the thermos and watch the pressure going up or you can connect a volumetric device and watch the volume increase while leaving the pressure at ambient.
Either way A at any time transfered energy to B and at no time was there an energy transfer from B to A. Else it should have been possible to observe a drop in pressure or volume.
The A ----> B energy transfer will continue until B is at the same final temperature f as A
Now you got the situation, σTf - σTf, where the energy transfer is null
After that both will start cooling down to the ambient temperature a ,because we can`t make a perfect thermos bottle.
The air in the thermos head space is now at the same volume and/or pressure it was when we started the process and now no more work or energy transfer between A and B is performed in either direction.
Warmers will refuse to accept that all Watts/m^2 = σT1 - σT^4 states is that cooling rate is slower. They claim that proves that A at T1 is getting energy from B at T2.
A Stirling engine performs less work per time, i.e. is loosing power when the cooling cycle is impeded even though you supply heat energy at the same rate as before.
According to the warmers that should not be happening because slowing the cooling rate means you added more heat energy.
According to the warmers, since photons are an energy quantum photons also have a mass.
After all E=mc^2 so it`s child`s play for warmers to find out the mass of a photon by solving for m, m=E/c^2 using the energy in photons to determine their mass.
Which gives us a clue how a Hollywood startrek photon torpedo works.
It`s a photon mass fusion reactor and the energy is the mass defect divided by c^2 after the fusion reaction.