KNOWLEDGE OF ENTROPY or ENTROPY OF KNOWLEDGE

 OECD PISA (OECD Program for International Student Assessment), which is widely discussed in Turkey with the results of its exams defines scientific literacy as follows in its framework study [1] in 2015:  "Scientific literate person  evaluates evidence and data, scientifically. She/he behaves according to the  scientifically explaining and questioning of a natural or technological event.  Scientific literacy does not require being a scientist or an educator in any discipline. As stated in the definition, it requires being able to speak with the method of science, as a "conscious citizen". This is, of course, the main educational problem.

If scientific literacy is not acquired in basic education;  the ease of accessing information sources  drives science enthusiasts into the error of speaking in scientific terms whose meanings they don't understand, and establishing a lot of incorrect analogies between everyday life and scientific theories. 

The most popular of these misuses is 'quantum', as most of us may have noticed. We realize that the quantum world, which is very distinct from our physically perceived world in scale, with its 'uncertainty', 'tunnel', and  'leap' is an 'entangled' (!) rumour  in many subjects from popular culture  to politics. Unfortunately, while a scientifically literate citizen should question such misuse, the assumption that speaking with this 'jargon' is scientific is settled.

There is another issue that the misuse of the terms, although not more common than the misuse of "quantum", prevents the establishment of basic scientific knowledge in a more destructive way: The Second Law of Thermodynamics! From the fact that life is finite, to the pain of death or the cure of this pain. Since the universe, which is an isolated  system, will disappear one day, problems of existence, belief disputes are being  discussed with high "entropy" (!), ranging from the arrow of time to the questioning of time. ‘No contradiction and misinformation in associating entropy with the dimension of life we perceive is being considered. But this is not 'Thermodynamics' or  'Thermodynamics' is not this!

JOURNEY OF CONCEPTS

  Thermodynamics has its own definitions, as in every branch of science. The formation and use of these definitions are in mutual interaction with the development of that branch. For example; The word "energy" used for the first time in 1807 by Thomas Yong (1773-1829) does not refer to "heat". It means the elastic energy of a spring and the potential and kinetic energies of the mass at its end. Therefore; we may think that using steam power to extract coal underground did not owe anything to thermodynamics until the end of the 18th century [2]. Although in Francis Bacon's (1561-1626) book 'heat' sources are mentioned [3], we can say that thermodynamics began with Joseph Black's (1728-1799) definition  of the concept of latent heat. Then James Watt separated the condenser from the piston-cylinder system of the steam engine (1769).

The idea of obtaining work from heat, later called the heat engine, was created by Carnot in 1824, as you know.  And the concept of entropy, was by Clausius in 1854. The "working substance"  in Carnot's famous booklet [4] can be accepted as the  first reference to the concept of "system" in terms of thermodynamics. 

'System' is a community  of objects. The working fluid (water / steam) in the heat machine, the refrigerant in the refrigerator, the gas in the cylinder can be taken as a 'system'.  In classical mechanics, 'system' is called  closed in case  it is "isolated" as if there is nothing other than itself [5].

 'System' is an example of confusing the definitions in classical mechanics with the thermodynamic definitions while trying to explain the concept of entropy with the analogy established with daily life and non-thermodynamic fields. In thermodynamics, a closed system does not mean an "isolated" system. In terms of thermodynamics, "closed system" means a system that does not exchange mass with its environment. But  work and heat exchange exist. In thermodynamics, the system that does not exchange mass, heat and work with its environment is called "isolated system". In other words, the "closed system" in classical mechanics is the "isolated" system in thermodynamics. Therefore, 'the entropy of a closed system increases with time' is a misrepresentation. 

(See https://singsurf.org/sorites/tidying.php)

The entropy of a closed or open system can increase or decrease. But; with the change in entropy of a closed or open system, the sum of the change in the entropy of its environment during this interaction is always in the positive direction.

ARRANGEMENT and DISORDER

Another word used in thermodynamic simulations is "disorder". "Disorder" is based on Wolfgang Boltzmann's definition of entropy on  micro scale in 1872. (In some sources, this definition of Boltzmann is not in 1872; the author used in 1877 [3]).

  What Boltzman says is this: Entropy is proportional to the logarithm of the number of microstates corresponding to a macro state. There are W cases where N1 molecules on one side and N2 molecules on the other will take place in a container divided into two (Figure 1).

(1)

According to the Boltzmann's relation, entropy is calculated as, where kB is the Boltzmann constant:

(2)

Figure 1 Distribution of molecules in a divided container

The number of microstates (Eqn. 1) takes the highest value when N1 = N2. Therefore, entropy (Eq. 2) is highest in equilibrium. This is essentially "Die Energie der Welt ist constant. Die Entropie der Welt strebt einem Maximum zu." by Clausius in 1865. (The energy of the universe is constant, its entropy is running towards the maximum). Since the universe is a thermodynamically isolated system, its entropy is constantly increasing.

The high number of micro states is a disorder at the molecular level. True! The higher the number of possible distributions of molecules, the greater the uncertainty. True! But; this is not identical with disorder in our daily life. It is wrong to draw an analogy between a messy room and a high entropy. (See https://singsurf.org/sorites/tidying.php))

MAXWELL'S DAEMON

The most important difference between classical mechanics and thermodynamics is that the governing equations in classical mechanics are also valid when the past and the future change places. The deterministic structure in classical mechanics is also valid when time is reversed. In short, classical mechanical equations are reversible. It is not for the laws of thermodynamics. Because; the real change of state  undergone by any closed or open system cannot be reversible.

To provide the reversibility; in 1867, James Clerk Maxwell (1831-1879) created an imaginary hero who  stood at the door between 2 compartments of equal temperature, initially (Figure 2), allowing each atom to pass from one compartment to the other according to its speed (kinetic energy). Thus,  daemon's decision based on the information would had been  able to make the process reversible.

Figure 2 Maxwell's daemon provides the reversibility!

According to Maxwell, the temperature difference between the 2 compartments could be recreated without any work, since the door opened and closed by this imaginary creature had very little mass. Of course, it cannot be ignored  that Maxwell's daemon  had information  about the speed (kinetic energy) of the atom, by paying a price with work. Therefore, this creature would not be able to overcome irreversibility either. This is a completed discussion. However, it is still used in anologies between thermodynamics and daily life and leads to misconception. It is very wrong to say, indeed,  that the person who is similar to daily life and tidies up a messy room can be identified with Maxwell's genie and reduces the entropy again, and pays the price of this reduction with his work.

(See https://singsurf.org/sorites/tidying.php)

CONCLUSION

Analogies between different fields may have negative effects; even though they have well-intentioned purposes such as making students like some lessons, giving examples from daily life to people who are distant to the subject and telling the facts. Thermodynamics can contain theories that cover many scientific fields in terms of content. But; as in every field, it is necessary to avoid the convenience of such analogous approaches, especially in scientific studies, especially in physics and especially in thermodynamics. Already; if there is enough thermodynamic competence to do these approaches correctly, then there exists also the knowledge that the analogies between the fields are an indicator of reductionism and scientific ignorance. Scientific literacy requires rigor.

REFERENCES

[1]  http://www.oecd.org/callsfortenders/Annex%20IA_%20PISA%202015%20Science%20Framework%20.pdf
[2]    Hall, A. R., Technology and Culture, Vol. 2, No: 4, (Autumn 1961), pp. 333-341.
[3]    Müller, I, A History of Thermodynamics, The Doctrine of Energy and Entropy, Springer, Berlin, 2006.
[4]    Müller I.'dan [3] aktarım: Carnot, S: [Reflections on the motive power of fire and on machines fitted to develop that power] à Paris chez Bachelier, Libraire. Quai des Augustin, No. 55 (1824). English translation by R.H. Thurston: ‘‘Reflections on the motive power of fire by Sadi Carnot and other papers on the second low of thermodynamics by É. Clapeyron and R. Clausius.” E. Mendoza (ed.) Dover Publ. New York (1960). pp. 1–59.
[5]    Susskind, L., Hrabovky, G., Classical Mechanics, The Theoretical Minimum, Penguin Books, GB, 2013.