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Pseudoscience in the American Journal of Physics

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Wikipedia quotes “Entropy and evolution” (Am. J. Phys., Vol. 76, No. 11, November 2008) to show that evolution does not violate the second law of thermodynamics.[1] The article incorrectly applies the Boltzmann equation for entropy to prove the second law is not violated.

Thermodynamics is a branch of physics based on the concept of temperature (T). Another basic variable is heat, which is what causes temperatures to change. Unlike temperature which is measured in degrees, heat is measured in joules, ergs, or kilowatt hours. Entropy (S) is defined with an integral equation in terms of heat and temperature. It is measured in joule/degrees.

Temperature is related to the statistical concept of the average kinetic energy of molecules (KE), and entropy is related to the concept of thermodynamic probability (W). The kinetic energy of a molecule is determined by its speed and mass. Thermodynamic probability can be understood by considering a system of non-interacting molecules in a container. If the gas has N molecules, imagine breaking up the container into N equal parts. The thermodyanic probability of all the molecules residing in one of the tiny compartments is one in N factorial (N(N-1)(N-2)...). The following equations describes the two relationships: KE=(3/2)kT and S=klogW. k is the Boltzmann constant and is determined experimentally to be 1.38 X 10-23 joule/degree.

The second law of thermodynamics is that a gas will fill up the entire container it is in because that is the most probable distribution of gas molecules. It is possible, but improbable, for all of the molecules to be huddled in one corner of the container. In other words, in an isolated thermodynamic system entropy will either increase or remain constant. If you compress a gas and extract heat from the gas, the entropy will decrease.




This kind of probabilistic calculation gives rise to the error that evolution violates the second law of thermodynamics. “Entropy and evolution” argues, quite irrationally, that evolution does not violate the second law because of the sun:


What the author, who thanked the peer-reviewers for helping him write the article, is trying to say is that entropy increases only for isolated systems not affected by outside forces or inputs. The sun is what caused the entropy of the biosphere to decrease during evolution. But as the article points out, heat from the sun increases entropy. The article makes no sense at all. The following quote from a peer-reviewed article explains why in more detail. Footnote 30 refers to "Entropy and evolution" and footnote 31 refers to "Evolution and the second law of thermodynamics" (Am. J. Phys., Vol. 77, No. 10, October 2009).

The preceding discussion has been concerning the formal expression of entropy reduction that can arise locally and such reasoning has often been used for proposing an ordering principle on the basis that an entropy increase elsewhere in the Universe ‘pays’ for the loss term locally (see Section 2 earlier). This idea is behind the work of Martyushev and Seleznev [13] and their maximum energy production principle (MEPP). It is also behind the idea of an ‘entropy flux’ which Styer [30] invokes for his calculations using the statistical definition of entropy (as a microcanonical ensemble of system states analogous to the Maxwell–Boltzmann theory of heat with a probability distribution of molecular vibrations). Both Styer [30] and Bunn [31] calculate by slightly different routes a statistical upper bound on the total entropy reduction necessary to ‘achieve’ life on earth. This is then compared to the total entropy received by the earth from a rate of solar radiation estimated to be absorbed by the earth for a given period of time. However, all these authors are making the same assumption – viz. that all one needs is sufficient energy flow into a closed system (or open system, where mass flow is allowed) and this will be the means of increasing the probability of life developing in complexity and new machinery evolving. But as stated earlier this begs the question of how a local system can possibly reduce the entropy without existing machinery to do this. It is this matter which is addressed in the next section – all important is the definition of what is meant by a machine. It will be seen that crucial to this whole issue is the inability of a given system to naturally raise the free energy locally without new machinery (and thus intelligence) being involved – machines need to be pre-existing to enable an increase in order and complexity to take place.

[McIntosh, A.C., "Information and entropy – top -down or bottom-up development in living systems?", Int. J. of Design & Nature and Ecodynamics. Vol. 4, No. 4 (2009) 351–385 – see in particular pp. 358,359, ]

However, it is one thing not to make sense, it is another thing to write down an incorrect equation in physics. The author considers organism A evolving into organism B over a period of 100 years, and estimates that organism B is 1000 times less probable than organism A. The author then uses this number to calculate the decrease in entropy with the Boltzmann constant and the equation for entropy. This is absurd because the Boltzmann constant comes from observations about atomic systems. The probability of shuffling a deck of cards and getting it back to its original factory order is one in 52! (i.e. 1 in 52 x 51 x 50 . . . x 2). It is nonsense to plug this number into the equation for entropy to calculate the entropy of a deck of cards in joule/degrees. Likewise, it is nonsense to calculate the entropy change of the biosphere in joule/degrees during evolution.

It may strikes some that the estimate of 1000 was not supported by any evidence. However, in a note titled “Evolution and the second law of thermodynamics,” the evolution of proteins was considered by a different author and the estimate of 1000 increased to 10199. This new calculation did not change the conclusion that evolution does not violate the second law of thermodynamics.


  1. Objections to evolution (Wikipedia)

See also