Corruption of Modern Physics 10: 2nd Law of Thermodynamics and Energy Crisis

The birth of modern physics is often described as Boltzmann's (attempted and failed) mathematical proof of a 2nd Law of Thermodynamics as the outstanding open problem of late 19th century physics, which introduced a new form of physics as statistical mechanics. This was picked up by Planck in his (attempted) proof of black body radiation, which led into the Born/Bohr Copenhagen interpretation of quantum mechanics based on statistics of atoms playing dice. 

The 2nd Law gives time a direction through the existence of irreversible processes characterised by an inevitable increase of a (mystical) quantity named entropy, which Boltzmann gave a statistical meaning as a tendency of physical processes to move from less probable to more probable states. Boltzmann struggled with the proof through all his life without coming to a resolution. 

In Computational Thermodynamics a New Proof of the 2nd Law is presented, which is not based on statistics but instead on the nature of turbulence as disordered small scale kinetic motion. 

The 2nd Law originally represented an empirical finding expressed by Carnot concerning the maximal efficiency $\eta$ of a heat engine such as a steam engine converting heat to mechanical energy when operating between temperatures $T_h$ and $T_c$ in Kelvin with $T_h>T_c$, of the form 

• $\eta =\frac{T_h-T_c}{T_h}$.  (0)  

This relation can be derived from the thermodynamic relation between change of internal (heat) energy $dE$ and mechanical work $pdV$ with $p$ pressure and $dV$ change of volume, of the form 

• $dE + pdV =0$.   (1)

stating that heat can be transferred to mechanical work only in expansion with $pdV>0$ and then $dE<0$.

We read from (0) that the efficiency $\eta$ of a heat engine increases with temperature difference $T_h-T_c$ (modulo losses).  Conversely, for a heat pump as a heat engine in reverse the efficiency $\frac{1}{\eta}$ decreases with increasing temperature difference. This makes a heat pump, in strong demand to meet the present Energy Crisis, inefficient when delivering hot water from outside air temperature below 0, while rather efficient (modulo losses) when delivering room temperature from ground temperature above 0.

Here (1) represents the balance of heat energy and work for an ideal process absent of losses. For a physical system it takes the following classical form used by Boltzmann

• $dE + pdV =TdS$,   (2)

where $T$ is temperature and $dS$ change of entropy $S$, while in the New Proof it takes the form

• $dE + pdV =Q$,   (3)

where $Q>0$ represents losses of turbulent nature. The essence of the 2nd Law in the form (2) is that $dS>0$ as inevitable increase of entropy. On the other hand, in the form (3) $Q>0$ expresses the inevitable appearance of turbulent dissipation as large scale kinetic motion turned into small scale kinetic motion appearing as heat energy which because of finite precision cannot be reversed, as an explanation of the direction of time exposed in The Clock and The Arrow; A Brief Theory of Time.

The basic problem confronting Boltzmann starting from (2) was to motivate why $dS>0$ and to this end he resorted to statistics seeking to connect a physical meaning to entropy $S$ as a measure of order with less ordered systems corresponding to more microstates $W$ being more probable than more ordered systems corresponding to fewer microstates, expressed on his grave stone as $S =\kappa logW$ with $\kappa$ Boltzmann's constant. This brought him into a lifelong struggle which ended in ultimate disorder hanging from a rope. 

The tragic continued with Planck followed by Born also resorting to statistics leading modern physics into a quagmire of roulette games. 

Bottom line: Nobody knows what is entropy based on statistics. Everybody can understand what is turbulent dissipation into heat. Atoms do what they have to do and are not left to decide themselves by playing dice. Compare with Corruption 5.

The main deficiency of classical thermodynamics based on (2), as compared to (3) with its New Proof, is that it considers different possible states with more or less entropy, but not the dynamics between states characterised by more or less entropy production, which is captured computationally in (3) as turbulent dissipation.