Entropy and the Arrow of Time

Summary

The second law of thermodynamics says that the total entropy of an isolated system never falls.  This article asks three questions about it.  Does evolution, or life itself, break it?  Why did the universe begin with so little entropy that the law has a direction at all?  And what do Boltzmann brains, the arrow of time and the heat death of the universe show?

1. Evolution does not violate the second law. The earth is not isolated. It absorbs sunlight and radiates the same energy to space as infrared, exporting at least 4.2 × 10¹⁴ joules per kelvin of entropy every second.
2. The budget is not close. Daniel Styer's estimate of what evolution needs, corrected by Styer himself, is about 3 J/K per second, a hundred-trillionth of the export. Emory Bunn's deliberately inflated ceiling on all life on earth is paid by sunlight in about 40 days. Redone with measured biomass it is paid in half a day to a day and a quarter. All the DNA on earth, counted as information, is worth 2.4 seconds of the export.
3. The argument's own advocates have stepped back from it. Henry Morris granted in 1974 that the sun supplies "certainly enough" energy and moved the question to how it is converted. Granville Sewell, the argument's most formal modern advocate, wrote in 2017 that his work "does not argue that evolution violates the second law." Answers in Genesis's physics page admits creationists have no "rigorously formulated entropy-based hypothesis," while charging that evolutionists have not shown the law permits evolution; Styer and Bunn did exactly that. Creation Ministries International's chemist advises creationists not to claim that evolution contradicts the second law.
4. "Disorder" and "information" are not entropy. Melted ice has more entropy than jumbled ice shards. Alloys, oil and vinegar and gases under gravity order themselves without life. Sewell's mathematical version holds, by his own account, only where "only heat conduction or diffusion is going on."
5. What survives is true, and it is not thermodynamics. Energy does nothing useful without a mechanism to direct it. Both sides agree. Whether unguided chemistry and selection supply that mechanism is a question for biology and probability, argued in other articles.
6. The universe's low-entropy beginning is real and unexplained. Today's observable universe holds about 10¹⁰⁴ k of entropy against a possible 10¹²³. Roger Penrose estimated that the beginning was special by a factor of 10¹⁰¹²³. Feynman, Albert and Wald agree that it has to be assumed rather than derived from known dynamics, and chance fluctuation does not explain it.
7. It fits creation without proving it. A chosen beginning would look like this. But Penrose's number is a ratio of volumes, not a probability, it is computed inside the big bang model, and Sean Carroll argues that the excess of low entropy counts against design. It shows that the present ordered era began a finite time ago, not that everything began, and it says nothing about the earth's age.
8. Boltzmann brains and heat death are constraints, not proofs. An eternal universe of random fluctuations would make lone fluctuating observers vastly outnumber evolved ones, which rules out chance as the source of the ordered past. Heat death is the physical future if nothing outside nature acts; Christian hope is a claim that something will.

Part 1: Does evolution violate the second law?

The argument, in the words of the people who made it

Henry Morris, the founder of the Institute for Creation Research, made the second law the heart of creationist physics.  In 1973 he wrote that "the law of increasing entropy is an impenetrable barrier which no evolutionary mechanism yet suggested has ever been able to overcome," and that "it is the Second law, however, that wipes out the theory of evolution."¹  His 1974 textbook Scientific Creationism said it "seems obvious that the Second Law of Thermodynamics constitutes a serious problem to the evolution model."²  In 1976 he called it "the most devastating and conclusive argument against evolution."³

Morris knew the standard reply:  the earth is not a closed box, and sunlight pours energy into it.  He called that reply "specious," "like arguing that, since NASA was able to put men on the moon, therefore it is reasonable to believe cows can jump over the moon!"³  He then restated the law in his own terms.  In any ordered system, he wrote, there is a tendency to decay, "which tendency can only be suspended or reversed by an external source of ordering energy directed by an informational program and transformed through an ingestion-storage-converter mechanism into the specific work required to build up the complex structure of that system."³  His table of "Criteria for Increasing Order" lists four:  an open system, available energy, a directing program and a conversion mechanism.³

Duane Gish, ICR's chief debater, put the same point in one line in 1993:  "an open system and an adequate outside source of energy are necessary but not sufficient conditions for the complexity, structure, and organization of a system to increase."⁴

The most formal modern version is by Granville Sewell, a mathematician at the University of Texas at El Paso.  His 2011 paper for Applied Mathematics Letters, accepted and then withdrawn before print, argues that the "compensation" reply "makes no sense logically," and ends:  "unless we are willing to argue that the influx of solar energy into the Earth makes the appearance of spaceships, computers and the Internet not extremely improbable, we have to conclude that the second law has in fact been violated here."⁵

Where the creationist organisations stand now

The two largest young-earth ministries have retired one version of the argument and kept the other.  Answers in Genesis lists "The Second Law of Thermodynamics Began at the Fall" among its arguments to avoid.⁶  Creation Ministries International lists the same claim among arguments creationists should not use, noting that "all beneficial processes in the world, including the development from embryo to adult, increase the overall disorder of the universe, showing that the Second Law is not inherently a curse."⁷  That is a claim about Genesis, and it is treated in Adam, the Fall, and Death.

On evolution, the same Answers in Genesis article says the opposite:  "Applying the second law of thermodynamics to various systems to refute evolutionary ideas is appropriate, but it must be done carefully and considering the concept of open and closed systems."⁶  Its current physics page on the subject, by the astronomer Danny Faulkner, calls the open-system reply "hand-waving and gross extrapolation."  Then it concedes:  "The problem for creationists is that we have yet to generate a rigorously formulated entropy-based hypothesis that clearly shows that life cannot arise through natural undirected processes."⁸  The same paragraph says evolutionists "generally have failed to produce a reasonable argument which agrees with observation that the second law of thermodynamics does not prohibit evolution."  The page cites neither Styer nor Bunn, whose published arguments are exactly that.  Creation Ministries International's chemist Jonathan Sarfati, quoted in the last section of this Part, advises creationists to stop claiming that the evolution of living things breaks the second law, but keeps the argument for the origin of the first life.

What the second law says

The second law, in its standard form, says that the total entropy of an isolated system never decreases.  An isolated system is one that exchanges neither energy nor matter with anything outside it.  Entropy has two standard definitions that agree.  In heat terms, a body that takes in heat Q at absolute temperature T gains entropy Q/T.  In counting terms, Ludwig Boltzmann's S = k ln Ω, where Ω is the number of microscopic arrangements consistent with what is seen and k is Boltzmann's constant, 1.38 × 10⁻²³ joules per kelvin.⁹

Nothing in the law forbids the entropy of one part of a system to fall.  A cup of hot coffee left on a table loses entropy as it cools, because heat leaves it.⁹  Water freezing in a pond, a seed growing into a tree and a child growing into an adult all lower the entropy of one region while raising it more somewhere else.  The law forbids only a net decrease for the isolated whole.

Creationist writers often quote the Harvard chemist John Ross, through Gish and Sarfati, to show that the law still holds for open systems:  "there are no known violations of the second law of thermodynamics.  Ordinarily the second law is stated for isolated systems, but the second law applies equally well to open systems."¹⁰  Ross is right, and nothing in the open-system reply denies it.  The reply is that the law applied to an open system must count the entropy that flows in and out.  Styer and Bunn apply it exactly that way, by drawing the boundary around the sun, the earth and the radiation leaving them.¹¹

The earth is not isolated.  It absorbs sunlight at about 5,800 K and sends the same energy back to space as infrared light at about 255 to 288 K.  That traffic carries entropy away from the planet, and the question is how much.

Morris did not dispute the quantity.  His own 1974 textbook says the open-system reply "confuses quantity of energy (of which there is certainly enough) with conversion of energy.  The question is not whether there is enough energy from the sun to sustain the evolutionary process;  the question is how does the sun's energy sustain evolution?"²  So the founder of the argument conceded the energy supply in 1974.  It is still worth pricing, because the popular version of the argument does not concede it.

The entropy budget, priced

Two physicists did the arithmetic in the American Journal of Physics.  Daniel Styer of Oberlin College published first, in 2008.⁹  Emory Bunn of the University of Richmond corrected him in 2009.¹¹  Both calculations were rerun for this article, and the script is published beside it.¹²

Styer's throughput.  Earth absorbs about 1.21 × 10¹⁷ watts of sunlight.  Dividing by the earth's mean surface temperature, 288 K, gives an entropy throughput of 4.20 × 10¹⁴ joules per kelvin every second.  Styer called this a lower bound.⁹  His table reproduces exactly.  Counting the radiation properly, with the 4/3 factor that applies to light and the earth's radiating temperature of 255 K, gives about 6.1 × 10¹⁴ J/K per second, 1.45 times more.¹²

Styer's requirement.  Styer assumed that "each individual organism is 1000 times 'more improbable' than the corresponding individual was 100 years ago," and that there are 10³² organisms on earth, a deliberate overestimate.⁹  That gives an entropy decrease of 9.53 × 10⁻²³ J/K per organism per century.  Styer printed the rate per second as 3.02 × 10⁻³⁰ J/K, and the biosphere's total as 302 J/K per second, "about one trillion times" smaller than the throughput.⁹

Styer's slip, and his correction.  The per-second figure is a hundred times too large.  Dividing 9.53 × 10⁻²³ J/K by the seconds in a century gives 3.02 × 10⁻³², not 10⁻³⁰;  the printed value divides by the seconds in one year.¹²  Styer published an erratum in 2014, and in 2015 he gave the corrected figure:  the decrease is "less than 3.02 J/K each second."^{13 14}  The error ran in the cautious direction.  On Styer's own assumptions the margin is about 10¹⁴, a hundred trillion, not a trillion.

Bunn's objection to Styer.  Bunn showed that Styer's factor of a thousand per century had no basis and was probably far too small.  Assembling just the proteins of one E. coli cell from free amino acids reduces the count of arrangements by a factor of about 10¹⁰⁹.  Spread over four billion years, that needs "a multiplicity reduction of ... 10²⁵ in each century, not 10³."¹¹  So Styer's specific numbers prove little.

Bunn's robust bound.  Bunn then set an upper limit that does not depend on any guess about evolution.  He compared the real earth with a "Dead-Earth" on which every atom of today's biomass sits in the atmosphere as simple gas, and he gave the living biomass zero entropy, which overstates the difference.  The result:  "the entropy reduction required for life on Earth is far less than |∆S_life| ∼ 10⁴⁴ k."  Sunlight supplies that in about 10⁷ seconds, "or less than a year.  Life on Earth took four billion years to evolve, so the second law of thermodynamics is safe."¹¹  His numbers reproduce.  The exact figure from his inputs is 40 days.¹²

The same bound with measured inputs.  Bunn rounded generously in one place and not in another.  He multiplied the carbon count by 100 for other elements.  His chemical potential, about −10 kT per molecule, is if anything too small:  computed for the real atmosphere it is about −24 kT for carbon dioxide and −19 kT for water vapour.  Redoing his method with the measured biomass, about 550 billion tonnes of carbon,¹⁵ one carbon dioxide and one water molecule drawn per carbon atom, and ideal-gas chemical potentials computed for the real atmosphere, gives 1.2 × 10⁴² k for the dry biomass and 3.1 × 10⁴² k with the water in the cells.  Sunlight pays that in 11.5 hours to 1.2 days.¹²

What the living world actually spends.  A second way to price it is to ask how much ordered chemical energy the whole biosphere makes each second.  Plants and plankton fix about 104.9 billion tonnes of carbon a year.¹⁶  Storing one mole of carbon as sugar takes about 478 kilojoules of free energy, one sixth of glucose's 2,870 kJ per mole.¹⁷  That is 1.3 × 10¹⁴ watts of stored free energy.  Expressed as entropy at 288 K, it is 4.6 × 10¹¹ J/K per second, about 0.1 % of the earth's throughput.¹²

What information costs.  The usual way to turn information into thermodynamic entropy is to count each bit as k ln 2.  Landenmark, Forgan and Cockell estimated all the DNA in the biosphere at 5.3 × 10³¹ megabases, which is 5.3 × 10³⁷ base pairs.¹⁸  At the maximum of two bits per base pair, that is 1.06 × 10³⁸ bits, worth 1.0 × 10¹⁵ J/K.  The earth exports that much entropy in 2.4 seconds.¹²  Writing every one of those bits at the theoretical minimum energy cost, kT ln 2 per bit, would take 2.4 seconds of the sunlight the earth absorbs.

The verdict on the quantitative claim is not close.  However the requirement is counted, by Styer's guesses, by Bunn's ceiling, by the free energy of all photosynthesis or by the information in all DNA, it is a vanishingly small fraction of what the earth exports every year, and most versions are paid within days or seconds.

Order, disorder and information

The popular argument runs on the word "disorder."  Entropy is often taught as disorder, and living things are obviously ordered, so evolution seems to run uphill.

Disorder is a teaching image, not the definition.  Styer:  "Disorder is a metaphor for entropy, not a definition for entropy."  His example:  smash ice cubes, toss the shards in a bowl and let them melt.  "The jumble of ice shards certainly seems more disorderly than the bowl of smooth liquid water, yet the liquid water has the greater entropy."⁹

Systems also order themselves while their total entropy rises, with nothing alive involved.  Oil and vinegar separate into layers.  An alloy of 30 % chromium in iron, held at 600 °C, does not stay uniform:  it separates on its own into a phase with about 22 % chromium and one with about 46 %.  A tall column of gas at one temperature is dense at the bottom and nearly empty at the top when it reaches equilibrium.¹⁴  Snow crystallizes, hurricanes grow out of scattered breezes and geysers spout.¹⁴  None of these is life, and Morris was right that crystals "have nothing whatever to do with evolution."³  They show something narrower:  that visible order and thermodynamic entropy are different things, so an argument that slides from one to the other proves nothing.

The same holds for information.  The information in a genome is a matter of which sequence is present.  Its thermodynamic cost, priced above at the maximum, is trivial.  If there is a barrier to new genetic information, it is not the second law.  Whether mutation and selection can add functional information is argued in When Evolution Creates Information and Measuring Biological Information.

Sewell's version, tested

Sewell's argument is the only one in this family written as mathematics, so it deserves a test on its own terms.

He starts from the equation for heat conducting through a solid.  Thermal entropy inside a region can fall only as fast as heat carries entropy out through its boundary.  He then defines an "X-entropy" for any substance X that diffuses, such as carbon in a solid, and gets the same inequality.  From it he concludes that X-order "can increase in only one way:  by importation through the boundary."⁵  Order of every kind, he argues, must be imported, and sunlight imports no computers.

His own paper states the limit of this result.  "Both equations are only valid for our simple models, where it is assumed that only heat conduction or diffusion is going on;  naturally, in more complex situations, the laws of probability do not make such simple predictions."⁵  A living cell is not a solid in which carbon only diffuses.  It is a chemical system in which reactions are driven by energy flows, and in which forces and flows of one kind push matter of another kind.  The counterexamples above break Sewell's rule even without life.  The iron-chromium alloy and the column of gas each increase their own "X-order" with no import of X at all.¹⁴

What is left is what Sewell calls a "tautology":  "If an increase in order is extremely improbable when a system is closed, it is still extremely improbable when the system is open, unless something is entering which makes it not extremely improbable."⁵  That is true, and it is not thermodynamics.  It is a statement about probability, and its force depends entirely on whether natural processes make complex life "not extremely improbable."  Sewell grants that this is the real dispute:  "one can still argue that the spectacular increase in order seen on Earth does not violate the second law because what has happened here is not really extremely improbable."⁵  That is exactly what biologists argue natural selection does.  The disagreement is real, but it belongs to biology and probability, not to the second law.

Sewell has said as much in print.  In 2001 he wrote:  "Thus one could argue that the origin and development of life may not have violated any of the laws of physics–only the laws of probability."¹⁹  In 2013 he granted that "all current statements of the second law apply only to isolated systems," proposed a wider principle, "Natural (unintelligent) forces do not do macroscopically describable things that are extremely improbable from the microscopic point of view," and noted "the similarity between (3b) and William Dembski's argument … that unintelligent forces do not do things that are 'specified' (simply or macroscopically describable) and 'complex' (extremely improbable)."²⁰  His 2017 paper in Physics Essays says it outright:  "Note that the article does not argue that evolution violates the second law, only that the compensation argument is logically invalid."²¹  What remains is a design argument stated in thermodynamic words.  It is tested where it belongs, in The Design Inference.  Styer's reply to the 2013 paper adds a list of things that are natural, macroscopically describable and wildly improbable at the level of molecules, from snowflakes to oak trees grown from acorns.¹⁴

The paper's withdrawal is a separate story, told in full in How Rare Is a Working Protein?.  In short, Applied Mathematics Letters accepted it in January 2011 and withdrew it before print.  The journal's later note apologised to Sewell and said the withdrawal was "not because of any errors or technical problems found by the reviewers or editors" but because the editor judged it more philosophical than mathematical.²²  That tells a reader the paper was not withdrawn for a mathematical error.  It does not tell a reader the argument is sound.

What survives: energy is necessary but not sufficient

One version of the argument is true.  Raw energy does not build machines.  Sunlight on a dead planet bleaches and cracks rock.  Gish said so:  "the flow of uncontrolled, raw energy into a system is destructive, not constructive."⁴  Morris's "directing program" and "conversion mechanism" name what turns energy into structure.³  Andy McIntosh, a combustion scientist at the University of Leeds and the creationist who has written most formally on the subject, puts it in the same terms.  He grants that the open-system reply "works for structures such as snowflakes that are formed by natural forces," but holds that "machines need to be pre-existing to enable an increase in order and complexity to take place."²³

The physicists who answer the argument agree.  Styer's own paper anticipates the point and answers it:  "The second law of thermodynamics permits but does not require evolution.  For example, the second law of thermodynamics holds on the Moon, yet biological evolution doesn't occur there."⁹  The founding book of the intelligent design movement on this subject, Thaxton, Bradley and Olsen's The Mystery of Life's Origin (1984), concluded that "it is thermodynamically possible to develop complex living forms, assuming the energy flow through the system can somehow be effective in organizing the simple chemicals into the complex arrangements associated with life."  The real question, for them, was that assumption:  how the coding work gets done.²⁴  Jonathan Sarfati, Creation Ministries International's physical chemist, wrote that he had "yet to see the calculations involving either heat transfer or Boltzmann microstates involved for natural selection.  Until creationists can do that, they should refrain from claiming that organic evolution contradicts the Second Law."  He still holds that second-law arguments are "strongest when dealing with chemical evolution," the origin of the first life.²⁵

So the surviving claim is this:  a mechanism is needed to turn energy into specified structure.  Both sides accept it.  For evolution after life exists, the mechanism the biologist proposes is plain:  cells already have a program, the genome, and a converter, metabolism, and the claim is that mutation and selection change the program.  Whether they can build new functional systems is a question about genetics, tested in the Observed Evolution articles.  For the origin of life, the question is whether chemistry could produce the first program and converter without them, which is the subject of The Origin of Life and How Rare Is a Working Protein?.  Neither question is answered by the second law, and calling them the second law has cost the creationist case credibility it did not need to lose.

Part 2: Why did the universe begin with low entropy?

The fact that needs explaining

The second law has a direction only because the universe's entropy is far below its maximum.  Chas Egan and Charles Lineweaver tallied it in 2010.  Today's observable universe holds about 3.1 × 10¹⁰⁴ k, almost all of it in the supermassive black holes at the centres of galaxies.  The photons of the cosmic background hold about 5.4 × 10⁸⁸ k.  The largest entropy the region could hold is about 10¹²³ k.  In their words, "That the increase of entropy has not yet been capped by some limiting value ... is the reason dissipative processes are ongoing and that life can exist."²⁶

Run the second law backwards and the past had lower entropy still.  Before stars formed and matter fell into black holes, the matter and radiation carried roughly 10⁸⁸ k, about what the background photons hold today.  For ordinary gases, spreading out raises entropy.  For matter under gravity, the reverse holds:  clumping into stars and black holes raises it.  So a hot, nearly perfectly smooth early universe, which looks like equilibrium, was in gravitational terms the most special state of all.  Roger Penrose put it this way:  "The 'lowness' of the entropy at the big bang — which gave us the second law — was thus not merely a consequence of the 'smallness' of the universe at the time of the big bang!"²⁷

Physicists agree that it needs explaining

The first proposed explanation was chance.  In 1895 Ludwig Boltzmann closed a letter to Nature with "an idea of my old assistant, Dr. Schuetz":  the universe as a whole sits forever in thermal equilibrium, and "If we assume the universe great enough, we can make the probability of one relatively small part being in any given state (however far from the state of thermal equilibrium), as great as we please."²⁸  The ordered region people see would then be a rare fluctuation.

Richard Feynman explained in 1963 why this fails.  "If our order were due to a fluctuation, we would not expect order anywhere but where we have just noticed it."  Every time astronomers look somewhere new, they find more order of the same kind.  "We therefore conclude that the universe is not a fluctuation, and that the order is a memory of conditions when things started.  This is not to say that we understand the logic of it."²⁹  Two years later he drew the conclusion that philosophers now use:  "I think it necessary to add to the physical laws the hypothesis that in the past the universe was more ordered, in the technical sense, than it is today."³⁰

The philosopher David Albert named that addition the "Past-Hypothesis":  "that the world first came into being in whatever particular low-entropy highly condensed big-bang sort of macrocondition it is that the normal inferential procedures of cosmology will eventually present to us."  He lists it as one of the three laws behind all of statistical mechanics.³¹  He believes it "not because it is entailed ... by any finite collection of particular empirical observations, but because of its conspicuous success."³¹

The leading physical idea for the early universe does not remove the need for it.  Cosmic inflation smooths the universe, but smoothing raises entropy, so inflation needs a still lower starting point.  Penrose:  such processes "do not explain the Second Law:  they use it."³²  The point, and the concession of it by one of inflation's founders, is set out in Cosmic Inflation.  Robert Wald of the University of Chicago, a leading relativist, argues more generally "that it is not plausible that these special initial conditions have a dynamical origin."³³

Penrose's number, priced

Penrose turned the specialness into a number.  He pictured "the Creator, armed with a 'pin' which is to be placed at some point in the phase space," where each point is a different possible starting state of the universe.²⁷  To find how small a target the Creator must hit, he took the roughly 10⁸⁰ protons and neutrons in the observable universe and asked what entropy they would have if collapsed into one black hole.  The Bekenstein-Hawking formula gives "a value of the order of 10¹²³."  Because entropy is the logarithm of a volume of possible states, the high-entropy states outnumber the low-entropy ones "by a factor that exceeds 10¹⁰¹²³."³⁴

The arithmetic checks.  A black hole holding 10⁸⁰ proton masses has an entropy of 7.4 × 10¹²² k, so the ratio is about 10 raised to the power 10^122.5.¹²  Starting from the early universe's 10⁸⁸ k instead of from zero changes nothing visible:  10⁸⁸ is one part in 10³⁵ of 10¹²³.  Sean Carroll and Jennifer Chen, using a smaller mass for the observable universe, get 10¹²¹ k for the maximum, "larger than the actual entropy by a factor of 10²²."³⁵  The two numbers differ only in the mass assumed.

Three limits on the number matter.

1. It is a ratio of volumes, not a probability. A ratio becomes a probability only if every starting state is assumed equally likely, and nobody knows what "equally likely" means for whole universes. The Berean Archive's fine-tuning article declines to treat such measures as chances, and this article follows it: the number shows how special the beginning was, not the odds of anything.
2. Penrose did not use it for design. He wrote that the anthropic principle "is virtually no help to us whatever in resolving our conundrum," and he proposed a new law, the Weyl Curvature Hypothesis, which says the beginning of the universe had to be smooth.^{34 27}
3. It is computed inside the big bang model. A reader who rejects that model loses the number. The underlying fact does not depend on it: stars are still burning, black holes are still growing, and the universe is nowhere near equilibrium today.

What the low-entropy beginning means for theism

The fact fits a created universe naturally.  If a mind chose the starting state, a special starting state is what one would expect, and the "Creator's pin" is Penrose's own picture.  Wald, who names no cause, still judges it "far more plausible that the answer to the above question as to why the very early universe was in a very low entropy state is that it came into existence in a very special state."  He adds at once:  "Of course, this answer begs the question, since one would then want to know why it came into existence in a very special state."³³

Chance is ruled out by Feynman's argument and by the Boltzmann-brain problem in Part 3.  That leaves two live answers.  One is a law of nature that fixes the beginning:  Albert's Past-Hypothesis taken as basic, or Penrose's Weyl Curvature Hypothesis.  The other is a choice.  Physics has not shown that the first is true, and it cannot show that the second is.

The strongest naturalist reply turns the size of the number against the theist.  Carroll:  "If anything, the much-more-than-anthropic tuning that characterizes the entropy of the universe is a bigger problem for the God hypothesis than for the multiverse.  If the point of arranging the universe was to set the stage for the eventual evolution of intelligent life, why all the grandiose excess represented by the needlessly low entropy at early times and the universe's hundred billion galaxies?"³⁶  Carroll is candid that the multiverse has not yet earned the point either:  showing that life in a multiverse typically follows a very low-entropy event "is a challenge, but not obviously an insuperable one."³⁶

The reply has two parts, one strong and one weaker.  The strong part:  the excess is exactly what rules out the anthropic and fluctuation explanations, as Penrose himself argues.  "From the purely anthropic point of view, this earlier far more special phase was not needed;  it would have been much more likely that our present 'improbable' stage came about simply by chance, rather than coming about via an earlier even more improbable stage."³⁴  A theory in which the universe is only as special as observers need is refuted by the excess.  The weaker part:  theism does not say the universe was made only to host life on one planet at minimum cost.  The biblical writers present the heavens as made to display their maker (Psalm 19:1), and a universe built to be explored by its inhabitants has reasons to be large and legible.  That reply is consistent but not predictive.  Theism does not predict 10¹²³.  A skeptic is right that the specific number was not forecast by anyone's theology.

What it means for a beginning

The oldest use of the second law in apologetics is the argument from the universe not having run down.  William Thomson, later Lord Kelvin, stated it in 1852:  "Within a finite period of time past, the earth must have been, and within a finite period of time to come the earth must again be, unfit for the habitation of man as at present constituted, unless operations have been, or are to be performed, which are impossible under the laws to which the known operations going on at present in the material world are subject."³⁷  Henry Morris's textbook put the cosmic version plainly:  "When all the energy of the cosmos has been degraded to random heat energy ... the universe will have died a 'heat death.'"  If the universe had existed forever under the present laws, it would already be dead.²  William Lane Craig gives the modern form:  "If in a finite amount of time, the universe will reach equilibrium, then, given infinite past time, it should by now already be in a state of equilibrium.  But it's not."³⁸  Craig also overstates one step.  He writes that "Contemporary physicists have universally rejected Boltzmann's daring many worlds hypothesis."  Carroll's survey says only that a theory dominated by fluctuating observers "is generally thought to be unacceptable, although opinions differ," and the 1895 idea was, by Boltzmann's own account, his assistant Schuetz's.^{38 39}

The argument proves less than it is often used for.  It shows that the present ordered era had a beginning a finite time ago.  Stars form from a finite supply of gas;  Fred Adams and Gregory Laughlin put the end of star formation at about 10¹⁴ years and the evaporation of the last black holes at 10⁶⁰ to 10¹⁰⁰ years, against an age now of about 10¹⁰.⁴⁰  It does not show that time, matter or the universe as a whole began.  Carroll and Chen's model, for example, has regions like ours budding off by inflation from empty space, with the process running "asymptotically both forwards and backwards in time," so that the whole has no first moment.³⁵  Such models are speculative, and none has independent support, but they show that the step from "the present order began" to "everything began" needs more than thermodynamics.  That step is argued, with its philosophical premises, in The Cosmological Argument.

The low-entropy beginning fits a young-earth reading as well as an old one, and it decides nothing between them.  It says the universe began in a special state.  It does not say when.

Part 3: The arrow of time, Boltzmann brains and heat death

The arrow of time

Arthur Eddington coined the phrase in 1928:  "I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space."⁴¹  He also gave the second law its famous rank.  It "holds, I think, the supreme position among the laws of Nature," and "if your theory is found to be against the second law of thermodynamics I can give you no hope;  there is nothing for it but to collapse in deepest humiliation."⁴¹  Creationist writers often quote that line against evolution.  Part 1 shows why it does not apply:  evolution is not found to be against the second law.

The basic laws of motion work the same forwards and backwards.  The direction of time that people experience, in which eggs break but do not unbreak and memories record the past but not the future, comes from the low-entropy beginning.  Albert:  "the reason there can be records of the past and not of the future is nothing other than that it seems to us that our experience is confirmatory of a past-hypothesis but not of any future one."³¹  So the arrow is not a separate puzzle.  It is the same fact as Part 2, seen from inside.

The arrow is used in apologetics in two ways.  Theists point out that the direction of time depends on a special beginning that the laws themselves do not supply, which is Part 2's argument again.  Naturalists sometimes argue that time itself is emergent, so that a "before" the universe makes no sense.  That is a question about the nature of time and about God's relation to it, treated in Time, Relativity, and Divine Eternity.

Boltzmann brains

The Boltzmann-Schuetz idea of Part 2 has a modern descendant.  If the universe lasts forever and keeps a small, steady temperature, rare fluctuations will keep happening forever.  The smallest fluctuation that contains an observer is not a whole ordered universe but a lone brain with false memories, a "Boltzmann brain."  Carroll defines it as "a configuration of matter that is (along with its local environment) as close as possible to thermal equilibrium, while still qualifying as an intelligent observer."³⁹

The numbers can be priced.  The universe is heading toward a state dominated by its vacuum energy, with a final temperature of about 2 × 10⁻³⁰ K.  At that temperature, a fluctuation that assembles one kilogram of matter is suppressed by a factor of about e^−3×1069.¹²  That is unimaginably rare.  But the time available is unlimited, and the horizon's entropy, about 3 × 10¹²² k, sets recurrence times of order e¹⁰¹²² years.^{42 12}  Ordinary observers can exist only while stars shine, which ends at about 10¹⁴ years.⁴⁰  Any finite suppression is eventually overcome by unlimited time, so a universe that lasts forever in this state produces infinitely many fluctuating observers and only finitely many evolved ones.

What follows is disputed, but not in a direction that helps chance.  Carroll argues that the problem is not that data refute such a theory, but that "the theories that predict them are cognitively unstable:  they cannot simultaneously be true and justifiably believed."³⁹  If most observers are fluctuations, a person's own memories and measurements, including the measurements that support the theory, are most likely illusions.  Don Page used the same reasoning to argue that the universe must decay within tens of billions of years, so that too few fluctuating observers are made:  "our universe is more likely than not to decay within a time that is less than 19 Gyr in the future."⁴³  Page added, in a footnote, that "A theistic explanation is that the universe was created by an omniscient God, so then at least God comprehends it."⁴³

Christian writers use Boltzmann brains against two targets.  Jeff Zweerink of Reasons to Believe, an old-earth ministry, argues that in a multiverse "the BBs far outnumber ordinary observers.  Thus, the typical observer in a multiverse should not see the well-ordered universe that we study."⁴⁴  The argument is fair against theories that make fluctuating observers typical, and it is the strongest reason, after Feynman's, to reject a chance origin of the low-entropy past.  It does not show that God exists.  Cosmologists treat it as a constraint that any good theory must meet, and several proposals meet it without God, for example by a decaying vacuum.  The multiverse question is treated in The Multiverse.

Heat death

Thomson's 1852 paper, quoted in Part 2, is also the first statement of the universe's end:  "There is at present in the material world a universal tendency to the dissipation of mechanical energy."³⁷  Modern cosmology keeps the conclusion and stretches the timescale.  Adams and Laughlin, writing in Reviews of Modern Physics, divide the future into eras measured in powers of ten of years.  Stars shine for about 10¹⁴ years.  Protons, if they decay at all, last more than 10³² years.  Black holes evaporate between 10⁶⁰ and 10¹⁰⁰ years.  After that, "cosmological heat death is postponed until after that epoch, i.e., until the Dark Era," when "it remains possible in principle for the universe to become nearly adiabatic and hence dull and lifeless."⁴⁰  Freeman Dyson once hoped that life could slow its metabolism and think forever.  Lawrence Krauss and Glenn Starkman showed that with a cosmological constant it cannot:  "Life must end, at least in the sense of being forced to have finite integrated subjective time."⁴⁵

Heat death is used for three arguments.

1. For a beginning. This is Thomson's argument, priced in Part 2. It is sound for the present ordered era and does not by itself reach the beginning of everything.
2. Against meaning. Bertrand Russell, in 1903: "all the labours of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the débris of a universe in ruins."⁴⁶ The physics behind Russell's premise has held up. The conclusion follows only if the physical future is the whole future, which is the point in dispute between Russell and the Christian.
3. As a biblical theme. Psalm 102:25-27, quoted in Hebrews 1:10-12, says the heavens will wear out like clothing while God remains. Isaiah 51:6 says the same. Read as physics, the verses fit the second law, but they are a statement about the creation's impermanence beside its maker, not a statement of thermodynamics, and they are fulfilled in Christian hope by a new creation (Romans 8:21, 2 Peter 3:13, Revelation 21:1), not by heat death. Physics predicts what happens if nothing outside nature acts. It cannot say whether something will.

Whether the second law began at the Fall, a claim both major young-earth ministries now reject, is treated in Adam, the Fall, and Death.

Objections and responses

"Raw energy destroys;  it does not build.  Sunlight alone cannot make a cell."  True, and nobody on either side disputes it.  Gish, Morris, McIntosh, Styer and Bunn all agree that energy is necessary but not sufficient.  The question is whether natural mechanisms can supply what else is needed.  That is a question about chemistry and genetics, not about the second law, and it is argued in the articles linked at the end of Part 1.

"Styer and Bunn count only thermal entropy.  The order in life is a different kind of entropy, and heat leaving the earth cannot pay for it."  This is Sewell's main claim, and his 2017 paper argues "that there is no such total entropy."²¹  Three replies.  First, statistical mechanics counts every kind of arrangement in one number:  Boltzmann's S = k ln Ω applies to chemical reactions, magnets and crystals as well as to heat.¹⁴  Second, Bunn's bound is not thermal.  It counts the cost of placing every atom of the biosphere into its exact quantum state, which is configurational entropy.  Third, one kind of order is routinely bought with another:  the alloy and the gas column of Part 1 order their atoms with no import of atomic order, because energy and forces couple the two.  If "information" is meant as a quantity that physics cannot exchange with anything else, it is no longer the second law, and the claim needs its own evidence.

"Crystals and snowflakes are not life."  Agreed.  Morris and McIntosh both say so, and this article cites crystals only to show that visible order and thermodynamic entropy are different things.

"A respected journal accepted Sewell's paper and then pulled it.  That shows suppression."  The journal itself said the withdrawal was not for any error found by reviewers or editors.  That clears the paper of a technical flaw found in review.  It does not make the argument right, and the argument's own author now says it does not show that evolution violates the second law.

"Bunn himself admits that creating all life in six days is thermodynamically problematic."  Bunn's footnote is a quip, and it fails on his own method.  His bound of 10⁴⁴ k was deliberately inflated.  With the measured biomass and computed chemical potentials, the same method gives 1 to 3 × 10⁴² k, which sunlight pays in half a day to a day and a quarter.¹²  An upper bound cannot show that anything is impossible.  Creation by God is also not a spontaneous process inside an isolated system, which is the only thing the second law constrains.

"Penrose's 10¹⁰¹²³ is meaningless without a probability measure, so you cannot infer anything."  Partly right, and this article does not use it as a probability.  The qualitative fact survives the objection:  the early universe was in a state of extremely low entropy, chance fluctuation does not explain it, and physicists from Feynman to Wald say it must be added to the laws as a separate assumption.

"Physics will find a law that fixes the initial state, and then there is nothing for God to do."  Possible.  Penrose's Weyl Curvature Hypothesis is such a proposal.  A law that singles out one extraordinarily special beginning would itself be a remarkable feature of the world, and the question of why the laws are as they are would remain.  But a skeptic is right that the low-entropy beginning is not a proof of God.  It is a fact that theism expects and naturalism must take as brute or explain by a law not yet found.

"The excess of low entropy counts against design."  This is Carroll's objection, answered in Part 2.  The excess is what rules out the anthropic and chance explanations.  It is not what theism would have predicted in advance, and the article says so.

"The not-yet-run-down argument assumes the present laws held forever.  Bounce and cyclic models escape it."  Correct.  The argument proves that the present ordered era began a finite time ago.  Whether everything began is a separate question.

Issues and unanswered questions

1. No agreed measure on initial states. Without one, Penrose's number cannot become a probability, and neither can any statement that the low-entropy beginning was "unlikely." This is the same limit the fine-tuning article applies to its tier-two evidence.
2. Sewell's generalized principle has no number in it. "Extremely improbable" and "macroscopically describable" are not defined well enough to test. Whether mutation and selection make complex life "not extremely improbable" is the real question, and it is argued in the biology articles, not here.
3. McIntosh's free-energy argument has no published physics reply that this research found. His claim is that biological machines need free energy raised in a way energy flow alone cannot do. It is a claim about mechanism, and the evidence on it is origin-of-life chemistry.
4. Two of Sewell's critics were not read in full. Jason Rosenhouse's 2001 reply in The Mathematical Intelligencer and Bob Lloyd's 2012 reply in the same journal were not obtained. Lloyd is known here only through Sewell's quotation of him. Styer's 2014 erratum was not read directly; its correction is known from Styer's 2015 note and matches this article's arithmetic.
5. The radiative entropy budget is a blackbody approximation. Detailed treatments of sunlight's spectrum and the atmosphere change the earth's entropy export by factors of order one. No version changes the verdict, which has margins of many orders of magnitude.
6. Two of Styer's appendix answers do not follow from their stated inputs. His problem 1 gives 10^4.17×108 from the stated inputs, not the printed 10^4.17×1012; his problem 2 needs about 60 million years, not the 54 stated, to give his printed answer.¹² Neither affects his main argument.
7. Whether Boltzmann-brain reasoning is valid is disputed. It assumes that observers should count themselves as typical, and philosophers disagree on whether that assumption is sound.
8. For a young-earth reader. Penrose's number and the early-universe entropy figures come from the big bang model. A young-earth cosmology needs its own account of why the universe is so far from equilibrium. Creation in a special state is that account, and it is a sufficient one, but it is not a prediction any young-earth model has made quantitatively.

Verdict

Evolution does not violate the second law of thermodynamics, and neither does the origin of life.  The earth exports entropy to space at about 4 × 10¹⁴ joules per kelvin every second.  Every honest estimate of what life needs, from Styer's corrected 3 J/K per second to Bunn's deliberately inflated ceiling, is paid by that export in a year or less, most of them in seconds to days.  Henry Morris conceded the energy budget in 1974.  Granville Sewell now says his work does not show that evolution violates the second law.  Answers in Genesis's own physics page admits that creationists have no rigorous entropy-based argument.  The argument should not be used.

What survives is true but is not the second law:  energy does nothing useful without a mechanism to direct it.  Whether unguided chemistry and natural selection can supply that mechanism is the real question, and it belongs to biology and probability.

The universe's low-entropy beginning is a different matter.  It is real, it is enormous, chance does not explain it, and physics currently takes it as an added assumption.  It is exactly what a created universe would show.  It does not prove creation, it does not reach past the beginning of the present ordered era by itself, and it says nothing about the age of the earth.  Boltzmann brains and heat death add constraints on cosmological theories and a sober picture of the physical future, but neither is an argument for God on its own.

Sources