Physical foundations of evolutionary theory

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Annila, A. & S.N. Salthe (2010) Physical foundations of evolutionary theory. Journal of Non-equilibrium Thermodynamics  35: 301-321,

13.02.2013 20:20


A small comment to the statement from the link above.

and that the idea of their improving rather than harming organisms is contrary to the Second Law of Thermodynamics, which tells us that matter and energy naturally tend toward greater randomness rather than greater order and complexity.”

I am afraid that this is a misunderstanding. The Second Law tells that the entropy increases in the isolated system. This is not the case with life on the Earth, as energy comes in and go out. In this case, if to speak of a system not far from the stationary state, Ilya Prigogine has proved that then the production of the entropy should be minimal. However, even this could not be generalized to the case when a system is far from equilibrium (this seems to be case with life on the Earth). Hence it is unlikely that the Second Law could help us when one considers evolution problems. In any case, I would recommend you the works of Ilya Prigogine – he was a great thermodynamicist.

13.02.2013 22:00

We should be careful when we consider the Universe. First it is unclear what the entropy of the Universe has to do with evolution on the Earth. Second, the normal thermodynamics is additive, that is, all the equations are derived under the assumption of

U = Sum_i U_i

This is definitely not the case for the Universe.

15.02.2013 20:26

Dear Stan,

I have browsed your paper. Unfortunately I was not able to follow your logic. One of the problems is that when we speak of the entropy, we must first define a thermodynamic system. To talk about the entropy without a well-defined thermodynamic system, in my view, does not make sense. Below I will consider two statements from your paper that seems to be important. I will show according to my understanding of the terminology that both statements are factually wrong. If I have misunderstood you, please correct me.

I should confess that I have missed your definition of the Second Law. In my considerations, I stay with that of Clausius, Kelvin and Gibbs. I believe that what they have developed is still valid.


p. 303 “A chemical reaction mixture is an example of an open system that will naturally progress toward the most probable, i.e., the maximum entropy, state.”

Let us first define a thermodynamic system. To this end, I will consider a gas mixture of 1 mole of hydrogen and 0.5 mole of oxygen at 298.15 K and 1 bar. I assume that that the system is closed in a sense that the mass transfer with environment is impossible due to unbreakable walls. The system is positioned in the environment that has 298.15 K and 1 bar. I further assume that the walls are made in such a way that the pressure in the system remains equal to that of surrounding (it is possible to imagine some piston that moves when required). The walls as such will be however neglected. This is not crucial, we could consider a system of constant volume as well or we could take walls into the consideration. Yet the mathematics below in the case of constant pressure and neglecting walls would be simpler. Finally I assume that the temperature and pressure of the environment remains constant. The latter is a normal assumption in thermodynamics.

A few standard definitions. A system is assumed to be closed when the mass transfer is impossible but it could exchange the energy with the environment.

A system is assumed to be open when the mass transfer is allows as well.

A system is assumed to be isolated when the mass transfer and energy exchange with the environment are impossible.

I believe that my systems should be covered by your statement, as a closed system is a special case of an open system. Now we assume that someone has introduced a catalyst into the system or we just wait long enough that the reaction will start on its own. Well, in our times when everybody is in a hurry, the catalyst would be a better solution.

A chemical reaction starts and proceeds spontaneously, that is, naturally. Now we estimate the change of the entropy in this process. From the NIST Webbook (or JANAF Thermodynamic Tables) the entropies per mole at 298.15 K and 1 bar {S^o_298 J/(mol*K)} are as follows

H2(g) 130.7
O2(g) 205.2
H2o(l) 70.0

Hence the change in the entropy of the process in question

H2(g) + 0.5 O2(g) = H2O(l)

Del S^o_298 = 70.0 – 130.7 – 0.5*205.2 = -163.3

is negative. Hence your statement if factually wrong. In my view, if it is wrong in one case, then we should just forget about it.


p. 307 “The 2nd law of thermodynamics in this form, as an equation of motion, is conceptually simple. It says: energy flows from heights to lows as soon as possible.”

Let us consider the thermodynamic system from above. We will not introduce a catalyst rather we will wait. In my view, this is a nice system with an interesting kinetics. It will stay without changes for long time and then presumably explodes (if we live long enough). In my view such a behavior contradict to your statement, that is, your statement again factually wrong.

Again, if the statement is wrong in one particular case, in my view, we should just forget it.


Let us be back to evolution. When we talk about evolution, a thermodynamic system presumably will be the biosphere. This is an open system (could be a closed system, depending on what we include in) but in any case it is not an isolated system. Hence, there is no thermodynamic reasons to state that the entropy of the biosphere increases. It may increase, it may decrease. It depends on the energy exchange with the surrounding and it has little to do with evolution.

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