You argue that my statement "Nature has a tendency towards the highest useful order" is speculative whimsy. I agree that it is arbitrary, but it is certainly not more speculative than what is written by scientists about entropy. It's not me who invented the strange link between entropy and order, nobody really understands. And I explain very carefully in which respect my conclusion is valid.

I defined 'entropy principle' in the following statement: "By equating disappearance of differences in temperature with disppearance of order, this law becomes as the entropy principle the antithesis of a final world view." It has no sense to make statements about 'the number of possible states', if the states are not given in a non-arbitrary way.

I would also argue that the appearence of solar systems lowered the entropy of empty space. Without such systems, there would be something similar to a homogeneous temperature radiation. But the radiation of stars and galaxies has differents temperatures and is not random.

That is really a big advantage for the dogma: There are no closed systems in universe. Billions of years have not been enough for the earth to remove a temperature difference of many hundreds of degrees Kelvin. In a dead star however, trillions of years are not enough for the differences to disappear.

Maybe you admit that the whole universe is a closed system. If yes, then order (and temperature differences) can only disappear, I see no other possibility than to conclude that the universe before the formation of galaxies was ordered at a higher degree than it is today.

If an egg relies on an energy input from outside, then the development of the chick in the egg is not only a refutation of the entropy principle, but even a complete refutation of the Second Law. There are several formulations of this law and one of them states that it is not possible to gain energy by simply cooling down something.

We can 'simulate' a closed system consisting of an egg in the centre and enough material of the needed temperature around. If you are right, then the egg can use thermal energy by cooling down the surrounding material! With a refrigerator, one cannot cool down a room, one only can heat it up.

I cannot agree with what you write about the the second law. My impression is that you rely too much on textbooks instead of dealing with the historical evolution of the concept 'entropy'. For writing a textbook it is not necessary to be a 'doer'. Most textbooks are more or less copies of other textbooks (Read ten textbooks and write the eleventh!). Even if you have found the same thing in several textbooks, it can be an error with a common source all the same.

As far as I know ('Energie und Entropie' by Falk and Ruppel, Springer, 1976, p. 91-92) the first who introduced the concept 'entropy' was Clausius in an attempt to write thermal energy as a product of an intensive and an extensive quantity. Because temperature was chosen as the intensive quantity, the extensive one was given by thermal energy divided by temperature. This concept has the physical unit 'joules per degree' or 'calories per degree' and was named entropy.

The mixture of a litre of water of 298° Kelvin and a litre of 302° gives two litres of 300°. The energy of the first litre is increased by 2 kcal, while the one of the second is decreased by 2 kcal. The entropy flow of the first litre is approximately 2000cal / 299°K = 6,69cal/°K while the one of the second is -2000cal / 301°K = -6.64cal/°K, and the total entropy flow is +0.044cal/°K.

Not even under the simple assumption that the thermal energy content of 'water' is proportional to its temperature, it would be possible to calculate the absolute entropy of 'water'. In order to halve the temperature of a litre, it is necessary to decrease the entropy by a certain value. In order to halve the temperature again, exactly the same amount of decrease in entropy is needed because both energy and temperature have been halved. One must conclude that absolute entropy is always infinite.

The original forms of the second law were formulated after engineers had noticed that there are always losses in thermal machines and that only temperature differences can be used as mecanical energy. If it were possible to gain usable energy from bodies or from lakes by simply cooling them down, there would be plenty of available energy. In 'Lexikon der Physik', Stuttgart, 1969, is given in addition to others the following formulation of the second law: "Ein perpetuum mobile 2. Art, eine Maschine, die nur durch Abkühlung eines Körpers Arbeit erzeugt, ins unmöglich (W.Ostwald)".

That's a very strange reasoning because losing thermal energy by radiation equals losing thermodynamic entropy. And it seems not very reasonable that a decreasing thermodynamic entropy can be an increasing logical entropy. Isn't your (and your scientist's) concept of entropy in fact a mixture of the concepts of thermodynamic entropy, logical entropy and energy?

In your second email you wrote: "There is no known way that any system can lower its entropy without an infusion of energy to cause the necessary changes." This statement is clearly wrong in the case of thermodynamic entropy!

Are you saying here that there is billions of times more mass in the universe not participating in the formation of planetary systems than participating?

I'm not sure that you are right. A collapse of a burnt-out star can lead to new nuclear reactions and for instance to a supernova. A prerequisite for the evolution of life was the formation of complex chemical elements in stars and supernovae. So evolutionary progress depends on the fact that solar systems appear and disappear. In any case, the formations and collapses of stars increase temperature differences and do not decrease them.

A general law is nothing more than a common expression for incountable concrete (conceivable) situations or relations. So I ask you: what is the 'available energy' of 1 kg of petrol of 30°Celsius in an environment of 0°Celsius? Is its 'total energy' 9*10^16 Joule (according to E=mc2)?

We can assume that the egg starts with the same temperature as the surrounding area. The point to explain is not the disappearance of the temperature difference between egg and surrounding area but the appearance of such a difference. Furthermore, a reduction in temperature always corresponds to a reduction in thermodynamic entropy.

The efficiency of ideal combustion engines is not very high (about 50% as far as I know). This fact gave rise to the original formulations of the second law. The digestive system uses chemical energy in a much more efficient way. The enzymes (or chemical reactions) building up a chick in an egg use chemical energy with an efficiency of even more than 100 percent (in the case the egg relies on an energy input from outside), because instead of producing waste heat they even absorb thermal energy. Such an efficiency of more than 100 percent is not compatible with the second law!

Even before the existence of refrigerators, earthenware vessels provided people with cool water. I do not claim that this is a refutation of the second law. Because water vaporizes on the whole surface of the vessel, water inside the vessel remains or gets cooler than the surrounding temperature. Why is this possible? Because of a selection process: the surface molecules with the highest energy vaporize.

Most time of my life I have been sure that a perpetuum mobile of the second kind is not possible, but now I'm no longer sure.

You also asked me to show you the math for my claim that absolute thermodynamic entropy is always infinite. That shows me that you don't understand at all the original concept of thermodynamic entropy. In my last email I explained that a reduction in temperature from 301° to 299° Kelvin of a litre of water leads to an entropy loss of about 2000 cal divided by 300° which results in 6,66 Clausius. Under the assumption that the thermal energy content of 'water' is proportional to its temperature, the entropy loss of a temperature reduction from 30.1° to 29.9° Kelvin is exactly the same: 200 cal / 30° = 6.66 Clausius. This infinity problem played an important role in the formulation of the third law (which seems to me a rather strange and arbitrary law).

The article recommended by Korthof shows that logical entropy is completely different from the original thermodynamic entropy. The current 'scientific' concept of entropy, the one you use, is an unclear mixture of these two concepts with further ingredients such as energy and order. You even equate "decreasing thermal entropy" with "decreasing unavailable energy". In this case the dimension of entropy would be both 'energy divided by temperature' and 'energy'. Entropy does not measure available or unavailable energy. Every body loses thermodynamic entropy by cooling down and gains entropy by heating up!

In a former email you wrote that "entropy is the mathematical inverse of the difference between the total and available energy of a system." This definition implies that entropy is dimensionless and that it is an intensive(!) quantity such as temperature. In your last email you explained how to calculate 'available' and 'total' energy, but you took into account neither kinetic nor gravity-potential energy. Is kinetic and potential energy (relative to the sun, to the centre of our galaxis and so on) 'available' energy or not?

The second law is relevant only to thermodynamics and all generalizations are totally unjustified. All such generalizations have nothing to do with reality, they are pure speculations! Absolutely nothing follows from this law for the evolution of the universe. What happens to a 'dead' star after having cooled down substantially, depends on things we do not know. In any case, black holes exist only in the brains of humans.

You write that an egg having the same temperature as the hen sitting on it would die. This cannot be true. Think about very little eggs which very rapidly adjust to the surrounding temperature or think about eggs heated up by the sun. There must be a certain temperature range which can be tolerated by a developing chick.

Your comments show a further time that you do not understand at all the (original) second law. This law is aequivalent to the impossibility of a perpetuum mobile of the second kind. What you write is exactly the contrary: thermal energy can be transformed into energy of chemical bonds. It would be possible to convert thermal energy without temperature differentials into chemical energy. If certain bonds are built up at a temperature of about 37° Celsius, there must be other bonds which can be built up at lower temperatures, e.g. 10° Celsius. In any container we could produce chemical energy by simply cooling down the environment!

By "absolute entropy" I mean something analogous to absolute (as opposed to 'relative') gravity-potential energy. According to classical physics absolute gravity-potential energy is always infinite, whereas according to my views it is exactly E = mc2. The term "absolute entropy" is a scientific one. You can find it at least in textbooks dealing with the history of the concept entropy.

In your addendum on entropy you write that "the Third Law is that no system can have a temperature below absolute zero". That seems absurd to me. For a temperature below zero to be possible, negative kinetic energy of atoms and molecules would be necessary!

In your email you write that the third law has experimentally been proven. You think that this is brilliant science. I think it is the contrary, because one cannot prove experimentally that there are no means to achieve absolute zero. At that temperature there are no relative motions between atoms or molecules.

I certainly do not need 'your' mistakes to conclude that scientists are in error. They make enough errors themselves. And not even secretely do I assume that e.g. Gert Korthof understands more about entropy than me. It may be the case that he or others understand more, but I believe only in what I understand myself. The only reason I mentioned that Korthof recommends the article of Brig Klyce is that I knew it would be important for you. I agree only partially with the article. The article clarifies that logical entropy does not measure (directly) order, but it fails to explain that there are (at least) two completely different concepts with the name '(normal, thermal or thermodynamic) entropy'.

A "quantitative measure of the amount of thermal energy not available to do work" should have the dimension of energy, but thermodynamic entropy has the dimension of energy divided by temperature! As far as I know, the available energy of a stone of 310°K at a surrounding temperature of 300°K is more or less the same as the one of an identical stone of 410°K at a surrounding temperature of 400°K. In the first case, however, the entropy difference is about 33% higher than in the second.

According to the ORIGINAL thermodynamic concept 'entropy' the following statements cannot be denied: "Entropy does not measure available or unavailable energy. Every body loses thermodynamic entropy by cooling down and gains entropy by heating up!"

And it is simply wrong that "thermal entropy is an actual measurement of energy" and that it "is usually given as joules (of unavailable energy) per degree (of temperature in Kelvins), since the temperature of a thermal system is directly proportional to the total thermal energy of that system, and it is easier to measure and employ temperature than to attempt to convert it, too, into joules." Furthermore, the temperature of a thermal system is generally NOT directly proportional to the total thermal energy of that system. Such a proportionality is only an idealisation! But even in the case of such a proportionality, the thermal energy content would depend on the mass of the system, whereas temperature would not.

You write: "But a ball of only 2 calories can have 2 calories of available energy, but only if the ball was surrounded by an infinite supply of matter or vacuum at absolute zero". Is any mechanism conceivable by which the 2 calories can be transformed into available energy? That would be in some respect an efficiency of 100% and such a high efficiency is, as far as I know, IN PRINCIPLE impossible. Therefore a petrol consuming engine cannot remain perfectly cool, and your claim that "the amount of available energy will always equal the total energy minus the equilibrium energy" is should be wrong.

Any mechanism by which it would be possible to produce pure hydrogen by cooling down e.g. sea water would be considered as a violation of the second law, because pure hydrogen is usable chemical energy. I do not know any chemical reactions which reduce the temperature of the environment. The disciplines thermochemistry and refrigeration technology deal with such questions. It is possible to cool down some liquids by dissolving salts, but that process is similar to cooling down by evaporation.