The 2nd Law as Radiative Heat Transfer

The 2nd Law of Thermodynamics states that heat energy $Q$ without forcing, is transferred from a body of temperature $T_1$ to a body of temperature $T_2$ with $T_1>T_2$ by conduction according to Fourier's Law if the bodies are in contact: 

• $Q =\gamma (T_1-T_2)$ 

and/or by radiation according Stephan-Boltzmann-Planck's Law if the bodies are not in contact as radiative heat transfer: 

• $Q=\gamma (T_1^4-T_2^4)$        (SBP)

where $\gamma > 0$.

The energy transfer is irreversible since it has a direction from warm to cold with $T_1>T_2$. It is here possible to view conduction as radiation at close distance and thus reduce the discussion to radiation. 

We can thus view the 2nd Law to be a consequence of (SBP), at least in the case of two bodies of different temperature: There is an irreversible transfer of heat energy from warm to cold. 

To prove 2nd Law for radiation thus can be seen to boil down to prove (SBF). This was the task taken on by the young Max Planck, who after a long tough struggle presented a proof in 1900, which he however was very unhappy with, since it like Boltzmann's H-theorem from 1872 was based on statistical mechanics and not classical deterministic physical mechanics.

But it is possible to prove (SBF) by replacing statistics with an assumption of finite precision computation in the form of  Computational Blackbody Radiation. Radiative heat transfer is here seen to be geared as a deterministic threshold phenomenon like a semi-conductor allowing heat transfer only one-way from warm to cold. 

Another aspect of radiation is that it is impossible to completely turn off or block by shielding of some sort. It connects to the universality of blackbody radiation taking the same form independent of material matter as shown here. 

We are thus led to the following form of the 2nd Law without any statistics:

• Radiative heat transfer from warm to cold is unstoppable and irreversible. 

The finite precision aspect here takes the form of a threshold, thus different from that operational in the case of turbulent dissipation into heat energy connecting to complexity with sharp gradients as discussed in recent posts.

PS To learn how statistical mechanics is taught at Stanford University by a world-leading physicist, listen to Lecture 1 and ask yourself if you get illuminated:

• Statistical mechanics is useful for predictions in cases when you do not know the initial conditions nor the laws of physics.