What is the Second Law of Thermodynamics?The laws of thermodynamics describe the relationships between thermal energy, or heat, and other forms of energy, and how energy affects matter. The First Law of Thermodynamics states that energy cannot be created or destroyed; the totalquantityof energy in the universe stays the same. The Second Law of Thermodynamics is about thequalityof energy. It states that as energy is transferred or transformed, more and more of it is wasted. The Second Law also states that there is a natural tendency of any isolated system to degenerate into a more disordered state.Saibal Mitra, a professor of physics at Missouri State University, finds the Second Law to be the most interesting of the four laws of thermodynamics. There are a number of ways to state the Second Law," he said. "At a very microscopic level, it simply says that if you have a system that is isolated, any natural process in that system progresses in the direction of increasing disorder, or entropy, of the system.Mitra explained that all processes result in an increase in entropy. Even when order is increased in a specific location, for example by the self-assembly of molecules to form a living organism, when you take the entire system including the environment into account, there is always a net increase in entropy. In another example, crystals can form from a salt solution as the water is evaporated. Crystals are more orderly than salt molecules in solution; however, vaporized water is much more disorderly than liquid water. The process taken as a whole results in a net increase in disorder.HistoryIn his book, "A New Kind of Science," Stephen Wolfram wrote, Around 1850 Rudolf Clausius and William Thomson (Lord Kelvin) stated that heat does not spontaneously flow from a colder body to a hotter body. This became the basis for the Second Law.Subsequent works byDaniel Bernoulli,James Clerk Maxwell, andLudwig Boltzmannled to the development of thekinetic theory of gases, in which a gas is recognized as a cloud of molecules in motion that can be treated statistically. This statistical approach allows for precise calculation of temperature, pressure and volume according to theideal gas law.This approach also led to the conclusion that while collisions between individual molecules are completely reversible, i.e., they work the same when played forward or backward, for a large quantity of gas, the speeds of individual molecules tend over time to form anormal or Gaussian distribution, sometimes depicted as a bell curve, around the average speed. The result of this is that when hot gas and cold gas are placed together in a container, you eventually end up with warm gas. However, the warm gas will never spontaneously separate itself into hot and cold gas, meaning that the process of mixing hot and cold gasses is irreversible. This has often been summarized as, You cant unscramble an egg. According to Wolfram, Boltzmann realized around 1876 that the reason for this is that there must be many more disordered states for a system than there are ordered states; therefore random interactions will inevitably lead to greater disorder.Work and energyOne thing the Second Law explains is that it is impossible to convert heat energy to mechanical energy with 100 percent efficiency. After the process of heating a gas to increase its pressure to drive a piston, there is always some leftover heat in the gas that cannot be used to do any additional work. This waste heat must be discarded by transferring it to a heat sink. In the case of a car engine, this is done by exhausting the spent fuel and air mixture to the atmosphere. Additionally, any device with movable parts produces friction that converts mechanical energy to heat that is generally unusable and must be removed from the system by transferring it to a heat sink. This is why claims for perpetual motion machines are summarily rejected by the U.S. Patent Office.When a hot and a cold body are brought into contact with each other, heat energy will flow from the hot body to the cold body until they reach thermal equilibrium, i.e., the same temperature. However, the heat will never move back the other way; the difference in the temperatures of the two bodies will never spontaneously increase. Moving heat from a cold body to a hot body requires work to be done by an external energy source such as aheat pump.The most efficient engines we build right now are large gas turbines, said David McKee, a professor of physics at Missouri State University. They burn natural gas or other gaseous fuels at very high temperature, over 2,000 degrees C [3,600 F], and the exhaust coming out is just a stiff, warm breeze. Nobody tries to extract energy from the waste heat, because theres just not that much there.

The arrow of timeThe Second Law indicates that thermodynamic processes, i.e., processes that involve the transfer or conversion of heat energy, are irreversible because they all result in an increase in entropy. Perhaps one of the most consequential implications of the Second Law, according to Mitra, is that it gives us the thermodynamic arrow of time.In theory, some interactions, such as collisions of rigid bodies or certain chemical reactions, look the same whether they are run forward or backward. In practice, however, all exchanges of energy are subject to inefficiencies, such as friction and radiative heat loss, which increase the entropy of the system being observed. Therefore, because there is no such thing as a perfectly reversible process, if someone asks what is the direction of time, we can answer with confidence that time always flows in the direction of increasing entropy.The fate of the universeThe Second Law also predicts the end of the universe, according toBoston University. "It implies that the universe will end in a heat death in which everything is at the same temperature. This is the ultimate level of disorder; if everything is at the same temperature, no work can be done, and all the energy will end up as the random motion of atoms and molecules.In the far distant future, stars will have used up all of their nuclear fuel ending up asstellar remnants, such as white dwarfs, neutron stars or black holes, according to Margaret Murray Hanson, a physics professor at the University of Cincinnati. They will eventually evaporate into protons, electrons, photons and neutrinos, ultimately reaching thermal equilibrium with the rest of the Universe. Fortunately, John Baez, a mathematical physicist at the University of California Riverside, predicts that thisprocess of cooling downcould take as long as 10(10^26)(1 followed by 1026(100 septillion) zeros) years with the temperature dropping to around 1030K (1030C aboveabsolute zero).Second Law of ThermodynamicsSecond Law of Thermodynamics - The Laws of Heat PowerThe Second Law of Thermodynamics is one of three Laws of Thermodynamics. The term "thermodynamics" comes from two root words: "thermo," meaning heat, and "dynamic," meaning power. Thus, the Laws of Thermodynamics are the Laws of "Heat Power." As far as we can tell, these Laws are absolute. All things in the observable universe are affected by and obey the Laws of Thermodynamics.

The First Law of Thermodynamics, commonly known as the Law of Conservation of Matter, states that matter/energy cannot be created nor can it be destroyed. The quantity of matter/energy remains the same. It can change from solid to liquid to gas to plasma and back again, but the total amount of matter/energy in the universe remains constant.Second Law of Thermodynamics - Increased EntropyThe Second Law of Thermodynamics is commonly known as the Law of Increased Entropy. While quantity remains the same (First Law), the quality of matter/energy deteriorates gradually over time. How so? Usable energy is inevitably used for productivity, growth and repair. In the process, usable energy is converted into unusable energy. Thus, usable energy is irretrievably lost in the form of unusable energy.

"Entropy" is defined as a measure of unusable energy within a closed or isolated system (the universe for example). As usable energy decreases and unusable energy increases, "entropy" increases. Entropy is also a gauge of randomness or chaos within a closed system. As usable energy is irretrievably lost, disorganization, randomness and chaos increase.Second Law of Thermodynamics - In the Beginning...The implications of the Second Law of Thermodynamics are considerable. The universe is constantly losing usable energy and never gaining. We logically conclude the universe is not eternal. The universe had a finite beginning -- the moment at which it was at "zero entropy" (its most ordered possible state). Like a wind-up clock, the universe is winding down, as if at one point it was fully wound up and has been winding down ever since. The question is who wound up the clock?

The theological implications are obvious. NASA Astronomer Robert Jastrow commented on these implications when he said, "Theologians generally are delighted with the proof that the universe had a beginning, but astronomers are curiously upset. It turns out that the scientist behaves the way the rest of us do when our beliefs are in conflict with the evidence." (Robert Jastrow,God and the Astronomers, 1978, p. 16.)

Jastrow went on to say, "For the scientist who has lived by his faith in the power of reason, the story ends like a bad dream. He has scaled the mountains of ignorance; he is about to conquer the highest peak; as he pulls himself over the final rock, he is greeted by a band of theologians who have been sitting there for centuries." (God and the Astronomers, p. 116.) It seems the Cosmic Egg that was the birth of our universe logically requires a Cosmic Chicken...The Second Law of ThermodynamicsWhat'sNEW

Morowitz

The use of thermodynamics in biology has a long history rich in confusion.HaroldJ.Morowitz(1)Sometimes people say that life violates the second law of thermodynamics. This is not the case; we know of nothing in the universe that violates that law. So why do people say that life violates the second law of thermodynamics? What is the second law of thermodynamics?The second law is a straightforward law of physics with the consequence that, in a closed system, you can't finish any real physical process with as much useful energy as you had to start with some is always wasted. This means that a perpetual motion machine is impossible. The second law was formulated after nineteenth century engineers noticed that heat cannot pass from a colder body to a warmer body by itself.According to philosopher of science Thomas Kuhn, the second law was first put into words by two scientists, Rudolph Clausius and William Thomson (Lord Kelvin), using different examples, in 1850-51(2). American quantum physicist Richard P. Feynman, however, says the French physicist Sadi Carnot discovered the second law 25 years earlier(3). That would have been before the first law, conservation of energy, was discovered! In any case, modern scientists completely agree about the above principles.Thermodynamic EntropyThe first opportunity for confusion arises when we introduce the termentropyinto the mix. Clausius invented the term in 1865. He had noticed that a certain ratio was constant in reversible, or ideal, heat cycles. The ratio was heat exchanged to absolute temperature. Clausius decided that the conserved ratio must correspond to a real, physical quantity, and he named it "entropy".Surely not every conserved ratio corresponds to a real, physical quantity. Historical accident has introduced this term to science. On another planet there could be physics without the concept of entropy. It completely lacks intuitive clarity. Even the great physicist James Clerk Maxwell had it backward for a while(4). Nevertheless, the term has stuck.TheAmerican Heritage Dictionarygives as the first definition of entropy, "For a closed system, the quantitative measure of the amount of thermal energy not available to do work." So it's a negative kind of quantity, the opposite of available energy.Today, it is customary to use the term entropy to state the second law:Entropy in a closed system can never decrease.As long as entropy is defined as unavailable energy, this paraphrase of the second law is equivalent to the earlier ones above. In a closed system, available energy can never increase, so (because energy is conserved) its complement, entropy, can never decrease.A familiar demonstration of the second law is the flow of heat from hot things to cold, and never vice-versa. When a hot stone is dropped into a bucket of cool water, the stone cools and the water warms until each is the same temperature as the other. During this process, the entropy of the system increases. If you know the heat capacities and initial temperatures of the stone and the water, and the final temperature of the water, you can quantify the entropy increase in calories or joules per degree.You may have noticed the words "closed system" a couple of times above. Consider simply a black bucket of water initially at the same temperature as the air around it. If the bucket is placed in bright sunlight, it will absorb heat from the sun, as black things do. Now the water becomes warmer than the air around it, and the available energy has increased. Has entropydecreased? Has energy that was previously unavailable become available, in a closed system? No, this example is only an apparent violation of the second law. Because sunlight was admitted, the local system was not closed; the energy of sunlight was supplied from outside the local system. If we consider the larger system, including the sun, available energy has decreased and entropy has increased as required.Let's call this kind of entropythermodynamic entropy. The qualifier "thermodynamic" is necessary because the word entropy is also used in another, nonthermodynamic sense.Logical EntropyEntropy is also used to mean disorganization or disorder. J. Willard Gibbs, the nineteenth century American theoretical physicist, called it "mixedupness." TheAmerican Heritage Dictionarygives as the second definition of entropy, "a measure of disorder or randomness in a closed system." Again, it's a negative concept, this time the opposite of organization or order. The term came to have this second meaning thanks to the great Austrian physicist Ludwig Boltzmann.Boltzmann

In Boltzmann's day, one complaint about the second law of thermodynamics was that it seemed to impose upon nature a preferred direction in time. Under the second law, things can only go one way. This apparently conflicts with the laws of physics at the molecular level, where there is no preferred direction in time an elastic collision between molecules would look the same going forward or backward. In the 1880s and 1890s, Boltzmann used molecules of gas as a model, along with the laws of probability, to show that there was no real conflict. The model showed that, no matter how it was introduced, heat would soon become evenly diffused throughout the gas, as the second law required.The model could also be used to show that two different kinds of gasses would become thoroughly mixed. The reasoning he used for mixing is very similar to that for the diffusion of heat, but there is an important difference. In the diffusion of heat, the entropy increase can be measured with the ratio of physical units, joules per degree. In the mixing of two kinds of gasses already at the same temperature, if no energy is dissipated, the ratio of joules per degree thermodynamic entropy is irrelevant. The non-dissipative mixing process is related to the diffusion of heat only by analogy(5). Nevertheless, Boltzmann used a factor,k, now called Boltzmann's constant, to attach physical units to the latter situation. Now the word entropy has come to be applied to the simple mixing process, too. (Of course, Boltzmann's constant has a legitimate use it relates the average kinetic energy of a molecule to its temperature.)Entropy in this latter sense has come to be used in the growing fields of information science, computer science, communications theory, etc. The story is often told that in the late 1940s, John von Neumann, a pioneer of the computer age, advised communication-theorist Claude E. Shannon to start using the term "entropy" when discussing information because "no one knows what entropy really is, so in a debate you will always have the advantage"(6).Richard Feynman knew there is a difference between the two meanings of entropy. He discussed thermodynamic entropy in the section called "Entropy" of hisLectures on Physicspublished in 1963(7), using physical units, joules per degree, and over a dozen equations (vol I section 44-6). He discussed the second meaning of entropy in a different section titled "Order and entropy" (vol I section 46-5) as follows:Feynman

Sowenowhave to talk about what we mean by disorder and what we mean by order. ... Suppose we divide the space into little volume elements. If we have black and white molecules, how many ways could we distribute them among the volume elements so that white is on one side and black is on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure "disorder" by the number of ways that the insides can be arranged, so that from the outside it looks the same.The logarithm of that number of ways is the entropy.The number of ways in the separated case is less, so the entropy is less, or the "disorder" is less.This is Boltzmann's model again. Notice that Feynman does not use Boltzmann's constant. He assigns no physical units to this kind of entropy, just a number (a logarithm.) And he uses not a single equation in this section of hisLectures.Notice another thing. The "number of ways" can only be established by first artificially dividing up the space into little volume elements. This is not a small point. In every real physical situation, counting the number of possible arrangements requires an arbitrary parceling. As Peter Coveney and Roger Highfield say(7.5):There is, however, nothing to tell us how fine the [parceling] should be. Entropies calculated in this way depend on the size-scale decided upon, in direct contradiction with thermodynamics in which entropy changes are fully objective.Shannon

Claude Shannon himself seems to be aware of these differences in his famous 1948 paper, "A Mathematical Theory of Communcation"(8). With respect to the parcelling he writes, "In the continuous case the measurement isrelative to the coordinate system. If we change coordinates the entropy will in general change" (p 37, Shannon's italics).In the same paper Shannon attaches no physical units to his entropy and never mentions Boltzmann's constant,k. At one point he briefly introducesK, saying tersely, "The constantKmerely amounts to a choice of a unit of measure" (p 11). Although the the 55-page paper contains more than 300 equations,Kappears only once again, in Appendix 2, which concludes, "The choice of coefficientKis a matter of convenience and amounts to the choice of a unit of measure" (p 29). Shannon never specifies the unit of measure.This sort of entropy is clearly different. Physical units do not pertain to it, and (except in the case of digital information) an arbitrary convention must be imposed before it can be quantified. To distinguish this kind of entropy from thermodynamic entropy, let's call itlogical entropy.The equationS = k logW + constappears without an elementary theory or however one wants to say it devoid of any meaning from a phenomenological point of view AlbertEinstein,1910(8.5)

In spite of the important distinction between the two meanings of entropy, the rule as stated above for thermodynamic entropy seems to apply nonetheless to the logical kind: entropy in a closed system can never decrease. And really, there would be nothing mysterious about this law either. It's similar to sayingthings never organize themselves. (The original meaning of organize is "to furnish with organs.") Only this rule has little to do with thermodynamics.It is true that crystals and other regular configurations can be formed by unguided processes. And we are accustomed to saying that these configurations are "organized." But crystals have not been spontaneously "furnished with organs." The correct term for such regular configurations is "ordered." The recipe for a crystal is already present in the solution it grows from the crystal lattice is prescribed by the structure of the molecules that compose it. The formation of crystals is the straightforward result of chemical and physical laws that do not evolve and that are, compared to genetic programs, very simple.The rule that things never organize themselves is also upheld in our everyday experience. Without someone to fix it, a broken glass never mends. Without maintenance, a house deteriorates. Without management, a business fails. Without new software, a computer never acquires new capabilities.Never.Charles Darwin understood this universal principle. It's common sense. That's why he once made a note to himself pertaining to evolution, "Never use the words higher or lower"(9). However, the word "higher" in this forbidden sense appears half a dozen times in the first edition of Darwin'sOrigin of Species(10).Even today, if you assert that a human is more highly evolved than a flatworm or anamoeba, there are darwinists who'll want to fight about it. They take the position, apparently, that evolution has not necessarily shown a trend toward more highly organized forms of life, just different forms: All extant species are equally evolved. Lynn Margulis and Dorion Sagan, 1995(11) There is no progress in evolution. Stephen Jay Gould, 1995(12) We all agree that there's no progress. Richard Dawkins, 1995(13) The fallacy of progress John Maynard Smith and Ers Szathmry, 1995(14)But this ignores the plain facts about life and evolution.

LifeisOrganizationSeen in retrospect, evolution as a whole doubtless had a general direction, from simple to complex, from dependence on to relative independence of the environment, to greater and greater autonomy of individuals, greater and greater development of sense organs and nervous systems conveying and processing information about the state of the organism's surroundings, and finally greater and greater consciousness. You can call this direction progress or by some other name.TheodosiusDobzhansky(15)Progress, then, is a property of the evolution of life as a whole by almost any conceivable intuitive standard.... Let us not pretend to deny in our philosophy what we know in our hearts to be true.EdwardO.Wilson(16)Life is organization. From prokaryotic cells, eukaryotic cells, tissues and organs, to plants and animals, families, communities, ecosystems, and living planets, life is organization, at every scale. The evolution of life is the increase of biological organization, if it is anything. Clearly, if life originates and makes evolutionary progress without organizing input somehow supplied, then something has organized itself. Logical entropy in a closed system has decreased. This is the violation that people are getting at, when they say that life violates the second law of thermodynamics. This violation, thedecreaseof logical entropy in a closed system, must happen continually in the darwinian account of evolutionary progress.Most darwinists just ignore this staggering problem. When confronted with it, they seek refuge in the confusion between the two kinds of entropy. [Logical] entropy has not decreased, they say, because the system is not closed. Energy such as sunlight is constantly supplied to the system. If you consider the larger system that includes the sun, [thermodynamic] entropy has increased, as required.Recent Writing About Entropy and BiologyAn excellent example of this confusion is given in a popular 1982 treatise against creationism,Abusing Science, by Philip Kitcher. He is aware that entropy has different meanings, but he treats them as not different: "There are various ways to understand entropy.... I shall follow the approach of classical thermodynamics, in which entropy is seen as a function of unusable energy. But the points I make will not be affected by this choice"(17).Another typical example of confusion between the two kinds of entropy comes from a similar book by Tim M. Berra,Evolution and the Myth of Creationism. The following paragraph from that book would seem to indicate that any large animal can assemble a bicycle(18).For example, an unassembled bicycle that arrives at your house in a shipping carton is in a state of disorder. You supply the energy of your muscles (which you get from food that came ultimately from sunlight) to assemble the bike. You have got order from disorder by supplying energy. The Sun is the source of energy input to the earth's living systems and allows them to evolve.A rare example of the use of mathematics to combine the two kinds of entropy is given inThe Mystery of Life's Origin, published in 1984. Its authors acknowledge two kinds of entropy, which they call "thermal" and "configurational." To count the "number of ways" for the latter kind of entropy they use restrictions which they later admit to be unrealistic. They count only the number of ways a string of amino acids of fixed length can be sequenced. They admit in the end, however, that the string might never form. To impose the units joules per degree onto "configurational" entropy, they simply multiply by Boltzmann's constant(19). Nevertheless, they ultimately reach the following conclusion (p 157-158):In summary, undirected thermal energy is only able to do the chemical and thermal entropy work in polypetide synthesis, but not the coding (or sequencing) portion of the configurational entropy work.... It is difficult to imagine how one could ever couple random thermal energy flow through the system to do the required configurational entropy work of selecting and sequencing.InEvolution, Thermodynamics and Information, Jeffrey S. Wicken also adopts the terms "thermal" and "configurational." But here they both pertain only to the non-energetic "information content" of a thermodynamic state, and "energetic" information is also necessary for the complete description of a system. Shannon entropy is different from all of these, and not a useful concept to Wicken. Nevertheless, he says that evolution and the origin of life are not separate problems and, "The most parsimonious explanation is to assume that life always existed"(19.5)!Roger Penrose's treatment of entropy is worth mentioning. InThe Emperor's New Mind(20), he nimbly dodges the problem of assigning physical units to logical entropy (p 314, Penrose's italics):In order to give theactualentropy values for these compartments we should have to worry a little about the question of the units that are chosen (metres, Joules, kilograms, degrees Kelvin, etc.). That would be out of place here, and in fact, for the utterly stupendous entropy values that I shall be giving shortly, it makes essentially no difference at all what units are in fact chosen. However, for definiteness (for the experts), let me say that I shall be takingnaturalunits, as are provided by the rules of quantum mechanics, and for which Boltzmann's constant turns out to beunity: k=1.Penrose

Someday in the future, an extension of quantum theory might provide a natural way to parcel any real physical situation. If that happens, one of the problems with quantifying logical entropy in a real physical situation will be removed. But nobody, not even Penrose, is suggesting that this is the case today. And even if that day comes, still we will have no reason to attach thermodynamic units to logical entropy. (Although the word "stupendous" appears again, no "actualentropy values" follow the quoted passage.) (Penrose, May 2012)InThe Refrigerator and the Universe(21), Martin Goldstein and Inge F. Goldstein wonder if there is "an irreconcilable difference" between the two kinds of entropy. They begin their consideration of logical entropy by discussing the possible arrangements of playing cards, where the parceling is not arbitrary the number of possibilities can be counted. When they move to the world of physics, they are not concerned over the fact that parceling must now be done arbitrarily. They are concerned, initially, about attaching physical units to logical entropy. "...Entropy is measured in units of energy divided by temperature....W[counting microstates] is a pure number" (p 173). But ultimately they apply Boltzmann's constant. No calculations using logical entropy with physical units ensue. The next time they mention logical entropy is in the section "Information and Entropy," where theydividethe previous product by Boltzmann's constant toremovethe physical units!An ambitious treatment of entropy as it pertains to biology is the bookEvolution as Entropy, by Daniel R. Brooks and E. O. Wiley. They acknowledge that the distinction between the different kinds of entropy is important(22):It is important to realize that the phase space, microstates, and macrostates described in our theory are not classical thermodynamic constructs.... The entropies are array entropies, more like the entropies of sorting encountered in considering an ideal gas than like the thermal entropies associated with steam engines....In fact the authors acknowledge many kinds of entropy; they describe physical entropy, Shannon-Weaver entropy, cohesion entropy, and statistical entropy, for example. They rarely use or mention Boltzmann's constant. One of their main arguments is that although the progress of evolution seems to represent a reduction in entropy, this reduction is only apparent. In reality, evolution increases entropy as the second law requires. But evolution does not increase entropy as fast as the maximum possible rate. So, by comparison to the maximum possible rate, entropyappearsto be decreasing. Our eyes have deceived us!In another book entitledLife Itself, mathematical biologist Robert Rosen of Columbia University seems to have grasped the problem when he writes, "The Second Law thus asserts that...a system autonomously tending to an organized state cannot be closed"(23). But immediately he veers away, complaining that the term "organization" is vague. Intent on introducing terms he prefers, like "entailment," he does not consider the possibility that, in an open system, life's organization could be imported into one region from another.Hans Christian von Baeyer's 1998 book,Maxwell's Demon, is engaging and informative about the scientists who pioneered the second law. The story concludes with an interview of Wojciech Zurek of the Theoretical Division of the Los Alamos National Laboratory. Zurek introducesanothersecond kind of entropy, because, "Like all scientific ideas, the concept of entropy, useful as it is, needs to be refurbished and updated and adjusted to new insights. Someday... the two types of entropy will begin to approach each other in value, and the new theory will become amenable to experimental verification"(23.5).Prigogine

One of the most profound and original treatments of entropy is that by the Nobel prize-winning chemist Ilya Prigogine. He begins by noticing that some physical processes create surprising patterns such as snowflakes, or exhibit surprising behavior such as oscillation between different states. InFrom Being To Becominghe says, in effect, that things sometimes do, under certain circumstances, organize themselves. He reasons that these processes may have produced life(24):It seems that most biological mechanisms of action show that life involves far-from-equilibrium conditions beyond the stability of the threshold of the thermodynamic branch. It is therefore very tempting to suggest that the origin of life may be related to successive instabilities somewhat analogous to the successive bifurcations that have lead to a state of matter of increasing coherence.Some find such passages obscure and tentative. One critic complains that work along the lines advocated by Prigogine fifteen years earlier has borne little fruit subsequently. "I don't know of a single phenomenon he has explained," said Pierre C. Hohenberg of Yale University(25).Dr. Hubert P. Yockey gives the subject of entropy and biology a probing and insightful treatment in his monograph,Information theory and molecular biology(26). He emphatically agrees that there are different kinds of entropy that do not correlate. "The Shannon entropy and the Maxwell-Boltzmann-Gibbs entropy... have nothing to do with each other" (p 313). But Shannon entropy (which pertains to information theory) makes no distinction between meaningful DNA sequences that encode life, and random DNA sequences of equal length. (Shannon wrote, "These semantic aspects of communication are irrelevant to the engineering problem.") With no distinction between meaningful and meaningless sequences, Yockey is able to conclude that evolution does not create any paradox for Shannon entropy. Nevertheless, Yockey proves with impressive command of biology and statistics that it would be impossible to find the new genes necessary for evolutionary progress by the random search method currently in favor. He is deeply sceptical of the prevailing theories of evolution and the origin of life on Earth. (Cynthia Yockey, 2005)Adami

In 1998, computer scientist Christoph Adami agrees that trouble dogs the marriage of biology and logical entropy. InIntroduction to Artificial Life(27), he comments on "the decades of confusion that have reigned over the treatment of living systems from the point of view of thermodynamics and information theory..." (p 59). He says, "information isalwaysshared between two ensembles" (p 70), a restriction that sounds promising. Yet in his section entitled "Second Law of Thermodynamics," he says that as a thermodynamic system is put into contact with another one at a lower temperature, and thermal equilibrium is reached, the total entropy of the combined ensemble "stays constant" (p 99). This flatly contradicts the second law. Later, applying the second law to information, he explains that only the "conditionalentropy" increases in such examples. "The unconditional (ormarginal) entropy given by conditional entropyplusmutual entropy... staysconstant" (p 118, Adami's italics). More new kinds of entropy.In 1999'sThe Fifth Miracle(28), theoretical physicist and science writer Paul Davies devotes a chapter, "Against the Tide," to the relationship between entropy and biology. In an endnote to that chapter he writes, "'higher' organisms have higher (notlower) algorithmic entropy..." (p 277, Davies' italics) another reversal of the usual understanding. He concludes, "The source of biological information, then, is the organism's environment" (p 57). Later, "Gravitationally induced instability is a source of information" (p 63). But this "still leaves us with the problem.... How hasmeaningfulinformation emerged in the universe?" (p 65). He gives no answer to this question.The Touchstone of Life(1999) follows Prigogine's course, relying on Boltzmann's constant to link thermodynamic and logical entropy(29). Author Werner Loewenstein often strikes the chords that accompany deep understanding. "As for the origin of information, the fountainhead, this must lie somewhere in the territory close to the big bang" (p 25). "Evidently a little bubbling, whirling and seething goes a long way in organizing matter.... That understanding has led to the birth of a new alchemy..." (p 48-49). Exactly.Medawar

ConclusionIn my opinion, the audacious attempt to reveal the formal equivalence of the ideas of biological organization and thermodynamic order ...must be judged to have failed.PeterMedawar(30)Computer scientist Rolf Landauer wrote an article published in June, 1996, which contains insight that should discourage attempts to physically link the two kinds of entropy. He demonstrates that "there is no unavoidable minimal energy requirement per transmitted bit"(31). Using Boltzmann's constant to tie together thermodynamic entropy and logical entropy is thus shown to be without basis. One may rightly object that the minimal energy requirement per bit of information is unrelated to logical entropy. But this supposed requirement was the keystone of modern arguments connecting the two concepts.Landauer

It is surprising that mixing entropy and biology still fosters confusion. The relevant concepts from physics pertaining to the second law of thermodynamics are at least 100 years old. The confusion can be eradicated if we distinguish thermodynamic entropy from logical entropy, and admit that Earth's biological system is open to organizing input from outside.

2nd Law of ThermodynamicsThe Second Law of Thermodynamics states that the state of entropy of the entire universe, as anisolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.IntroductionWhy is it that when you leave an ice cube at room temperature, it begins to melt? Why do we get older and never younger? And, why is it whenever rooms are cleaned, they become messy again in the future? Certain things happen in one direction and not the other, this is called the "arrow of time" and it encompasses every area of science. The thermodynamic arrow of time (entropy) is the measurement of disorder within a system. Denoted asSS, the change of entropy suggests that time itself is asymmetric with respect to order of an isolated system, meaning: a system will become more disordered, as time increases.Major players in developing the Second Law Nicolas LonardSadi Carnot was a French physicist, who is considered to be the "father of thermodynamics," for he is responsible for the origins of the Second Law of Thermodynamics, as well as various other concepts. The current form of the second law uses entropy rather than caloric, which is what Sadi Carnot used to describe the law. Caloric relates to heat and Sadi Carnot came to realize that some caloric is always lost in the motion cycle. Thus, the thermodynamic reversibility concept was proven wrong, proving that irreversibility is the result of every system involving work. Rudolf Clausius was a German physicist, and he developed the Clausius statement, which says "Heat generallycannot flow spontaneouslyfrom a material at a lower temperature to a material at a higher temperature." William Thompson, also known as Lord Kelvin, formulated the Kelvin statement, which states "It isimpossibleto convert heat completely in a cyclic process." This means that there is no way for one to convert all the energy of a system into work, without losing energy. Constantin Carathodory, a Greek mathematician, created his own statement of the second low arguing that "In the neighborhood of any initial state, there are states whichcannotbe approached arbitrarily close through adiabatic changes of state."Fig. 1:Nicolas Carnot (left), Rudolf Clausius (second on left), William Thompson (second on right),Constantin Carathodory (right)ProbabilitiesIf a given state can be accomplished in more ways, then it is more probable than the state that can only be accomplished in a fewer/one way.Assume a box filled with jigsaw pieces were jumbled in its box, the probability that a jigsaw piece will land randomly, away from where it fits perfectly, is very high. Almost every jigsaw piece will land somewhere away from its ideal position. The probability of a jigsaw piece landing correctly in its position, is very low, as it can only happened one way. Thus, the misplaced jigsaw pieces have a much higher multiplicity than the correctly placed jigsaw piece, and we can correctly assume the misplaced jigsaw pieces represent a higher entropy.Derivation and ExplanationTo understand why entropy increases and decreases, it is important to recognize that two changes in entropy have to considered at all times. The entropy change of the surroundings and the entropy change of the system itself. Given the entropy change of the universe is equivalent to the sums of the changes in entropy of the system and surroundings:Suniv=Ssys+Ssurr=qsysT+qsurrT(1)(1)Suniv=Ssys+Ssurr=qsysT+qsurrTIn an isothermal reversible expansion, the heat q absorbed by the system from the surroundings isqrev=nRTlnV2V1(2)(2)qrev=nRTlnV2V1Since the heat absorbed by the system is the amount lost by the surroundings,qsys=qsurrqsys=qsurr.Therefore, for a truly reversible process, the entropy change isSuniv=nRTlnV2V1T+nRTlnV2V1T=0(3)(3)Suniv=nRTlnV2V1T+nRTlnV2V1T=0If the process is irreversible however, the entropy change isSuniv=nRTlnV2V1T>0(4)(4)Suniv=nRTlnV2V1T>0If we put the two equations forSunivSunivtogether for both types of processes, we are left with the second law of thermodynamics,Suniv=Ssys+Ssurr0(5)(5)Suniv=Ssys+Ssurr0whereSunivSunivequals zero for a truly reversible process and is greater than zero for an irreversible process. In reality, however, truly reversible processes never happen (or will take an infinitely long time to happen), so it is safe to say all thermodynamic processes we encounter everyday are irreversible in the direction they occur.NoteThe second law of thermodynamics can also be stated that "allspontaneousprocesses produce anincreasein the entropy of the universe".Gibbs Free EnergyGiven another equation:Stotal=Suniv=Ssurr+Ssys(6)(6)Stotal=Suniv=Ssurr+SsysThe formula for the entropy change in the surroundings isSsurr=Hsys/TSsurr=Hsys/T. If this equation is replaced in the previous formula, and the equation is then multiplied by T and by -1 it results in the following formula.TSuniv=HsysTSsys(7)(7)TSuniv=HsysTSsysIf the left side of the equation is replaced byGG, which is know as Gibbs energy or free energy, the equation becomesG=HTS(8)(8)G=HTSNow it is much simpler to conclude whether a system is spontaneous, non-spontaneous, or at equilibrium. HHrefers to the heat change for a reaction. A positiveHHmeans that heat is taken from the environment (endothermic). A negativeHHmeans that heat is emitted or given the environment (exothermic). GGis a measure for the change of a system's free energy in which a reaction takes place atconstantpressure (PP) and temperature (TT).According to the equation, when the entropy decreases and enthalpy increases the free energy change,GG, is positive and not spontaneous, and it does not matter what the temperature of the system is. Temperature comes into play when the entropy and enthalpy both increase or both decrease. The reaction is not spontaneous when both entropy and enthalpy are positive and at low temperatures, and the reaction is spontaneous when both entropy and enthalpy are positive and at high temperatures. The reactions arespontaneous when the entropy and enthalpy are negative at low temperatures, and the reaction is not spontaneous when the entropy and enthalpy are negative at high temperatures. Because all spontaneous reactions increase entropy, one can determine if the entropy changes according to the spontaneous nature of the reaction (Equation 8).Table 1:Matrix of Conditione Dictating Spontaneity

CaseHHSSGGAnswer

high temperature-+-Spontaneous

low temperature-+-Spontaneous

high temperature--+Nonspontaneous

low temperature---Spontaneous

high temperature++-Spontaneous

low temperature+++Nonspontaneous

high temperature+-+Nonspontaneous

low temperature+-+Nonspontaneous

Example 1Lets start with an easy reaction:2H2(g)+O2(g)2H2O(g)2H2(g)+O2(g)2H2O(g)The enthalpy,HH,for this reaction is -241.82 kJ, and the entropy,SS,of this reaction is -233.7 J/K. If the temperature is at 25 C, then there is enough information to calculate the standard free energy change, GG.The first step is to convert the temperature to Kelvin, so add 273.15 to 25 and the temperature is at 298.15 K. Next plugHH,SS, and the temperature into theG=HTSG=HTS.GG= -241.8 kJ + (298.15 K)(-233.7 J/K)=-241.8 kJ + -69.68 kJ (Don't forget to convert Joules to Kilojoules)= -311.5 kJExample 2Here is a little more complex reaction:2ZnO(s)+2C(g)2Zn(s)+2CO(g)2ZnO(s)+2C(g)2Zn(s)+2CO(g)If this reaction occurs at room temperature (25 C) and the enthalpy,HH, and standard free energy,GG, is given at -957.8 kJ and -935.3 kJ, respectively. One must work backwards somewhat using the same equation from Example 1 for the free energy is given.-935.3 kJ =-957.8 kJ + (298.15 K) (SS)22.47 kJ =(298.15 K) (SS) (Add-957.8 kJ to both sides)0.07538 kJ/K =SS (Divide by298.15 K to both sides)Multiply the entropy by 1000 to convert the answer to Joules, and the new answer is 75.38 J/K.Example 3For the following dissociation reactionO2(g)2O(g)O2(g)2O(g)under what temperature conditions will it occurs spontaneously?SOLUTIONBy simply viewing the reaction one can determine that the reaction increases in the number of moles, so the entropy increases. Now all one has to do is to figure out the enthalpy of the reaction. The enthalpy is positive, because covalent bonds are broken. When covalent bonds are broken energy is absorbed, which means that the enthalpy of the reaction is positive. Another way to determine if enthalpy is positive is to to use the formation data and subtract the enthalpy of the reactants from the enthalpy of the products to calculate the total enthalpy. So, if the temperature is low it is probable thatHHis more thanTSTS, which means the reaction is not spontaneous. If the temperature is large thenTSTSwill be larger than the enthalpy, which means the reaction is spontaneous.Example 4The following reactionCO(g)+H2O(g)CO2(g)+H2(g)CO(g)+H2O(g)CO2(g)+H2(g)occurs spontaneously under what temperature conditions? The enthalpy of the reaction is -40 kJ.SOLUTIONOne may have to calculate the enthalpy of the reaction, but in this case it is given. If the enthalpy is negative then the reaction is exothermic. Now one must find if the entropy is greater than zero to answer the question. Using the entropy of formation data and the enthalpy of formation data, one can determine that the entropy of the reaction is -42.1 J/K and the enthalpy is -41.2 kJ. Because both enthalpy and entropy are negative, the spontaneous nature varies with the temperature of the reaction. The temperature would also determine the spontaneous nature of a reaction if both enthalpy and entropy were positive. When the reaction occurs at a low temperature the free energy change is also negative, which means the reaction is spontaneous. However, if the reaction occurs at high temperature the reaction becomes nonspontaneous, for the free energy change becomes positive when the high temperature is multiplied with a negative entropy as the enthalpy is not as large as the product.Example 5Under what temperature conditions does the following reaction occurs spontaneously ?H2(g)+I(g)2HI(g)H2(g)+I(g)2HI(g)SOLUTIONOnly after calculating the enthalpy and entropy of the reaction is it possible for one can answer the question. The enthalpy of the reaction is calculated to be -53.84 kJ, and the entropy of the reaction is 101.7 J/K. Unlike the previous two examples, the temperature has no affect on the spontaneous nature of the reaction. If the reaction occurs at a high temperature, the free energy change is still negative, andGGis still negative if the temperature is low. Looking at the formula for spontaneous change one can easily come to the same conclusion, for there is no possible way for the free energy change to be positive. Hence, the reaction is spontaneous at all temperatures.Application of the Second LawThe second law occurs all around us all of the time, existing as the biggest, most powerful, general idea in all of science.Explanation of Earth's AgeWhen scientists were trying to determine the age of the Earth during 1800s they failed to even come close to the value accepted today. They also were incapable of understanding how the earth transformed. Lord Kelvin, who was mentioned earlier, first hypothesized that the earth's surface was extremely hot, similar to the surface of the sun. He believed that the earth was cooling at a slow pace. Using this information, Kelvin used thermodynamics to come to the conclusion that the earth was at least twenty million years, for it would take about that long for the earth to cool to its current state. Twenty million years was not even close to the actual age of the Earth, but this is because scientists during Kelvin's time were not aware of radioactivity. Even though Kelvin was incorrect about the age of the planet, his use of the second law allowed him to predict a more accurate value than the other scientists at the time.Evolution and the Second LawSome critics claim that evolution violates the Second Law of Thermodynamics, because organization and complexity increases in evolution. However, this law is referring to isolated systems only, and the earth is not an isolated system or closed system. This is evident for constant energy increases on earth due to the heat coming from the sun. So, order may be becoming more organized, the universe as a whole becomes more disorganized for the sun releases energy and becomes disordered. This connects to how the second law and cosmology are related, which is explained well in the video below.