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The relationship between entropy and life is complex and has even "philosophical" ramifications. The following thought experiment seems simple enough to bring a clear answer, but I'm unsure of my conclusions and would appreciate some help.

(A) Let's imagine the following open system: a box containing a quantity of atoms - C, H, O, and so on, the usual suspects, in whatever random spatial distribution. The system is open because it receives energy in the form of radiation in the visible spectrum, and it radiates energy outwards so that the temperature $T$ in the box remains stable.

The principles of thermodynamics imply that temperature $T$, energy $E_A$, local entropy $s_A$ in that box remain constant. Global entropy $S_A$ increases since incoming energy dissipates in the rest of the universe.
Is this correct?

(B) Imagine the same box, same incoming radiations. But this time atoms are organised in molecules and cells allowing photosynthesis to take place in the box.

$T$ is still constant, but $E_B$ the energy in the box is increasing, since part of the incoming energy is stored chemically as additional organic material. Therefore energy dissipated into space is lower compared to (A). Local entropy $s_B$ decreases, since atoms are forced into a specific organisation, reducing the number of possible microstates. Is this correct?

Global entropy $S_B$ still increases. But does it increase less than $S_A$?

(Related questions : Local decrease of entropy, does it require life? ; Can life decrease the entropy of an isolated system? )

stuffu
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YAG
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2 Answers2

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Let's first consider some basics. Does a mirror produce entropy when light shines on it? No, the entropy of the light bounces off of the mirror, or reflects.

Does a broken mirror, that looks white, produce entropy when light hits it? No, the information about the disordered pieces of class is copied into the light, many times, if the bean is long. A repeating pattern is not disorder.

Does a black object produce entropy, when light heats it, and then the object emits infrared light? Yes.

Now we can discuss the box. Let's say the box consists of small black spots, and small white spots, looking gray to the naked eye.

The idea here is that a dark-gray object is made of 10% perfectly white spots and 90% perfectly black spots, while a light-gray object is made of 90% perfectly white spots and 10% perfectly black spots.

Now let's suppose gray-colored life appears on the white spots. That life can't be perfectly white, so entropy radiating from the box to space must increase. (That life consists of black spots and white spots, the black spots can not convert 100% of thermal energy of sun-light to non-thermal energy, according to the second law of thermodynamics, so the life must radiate some thermal energy and that thermal energy must contain entropy)

Let's suppose gray colored life appears on the black spots. That life's white spots do not produce entropy, and that life's black spots radiate less energy and entropy than the black spot that the the life is living on.

So this life decreases the entropy radiated to space.

stuffu
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Let me first point out that the entropy production in non-equilibrium open systems has been studied - it is not fully understood, but some things are known - see, e.g., the discussion in thread Maximum Principle vs. Minimum Principle in Non-equilibrium Thermodynamics

Now, we consider situation A no chemical reactions take place, whereas in situation B some new molecules are formed. A few points to note:

  • Situation A eventually evolves to a stationary state - the "box" receives as much energy as it dissipates into the environment. Note that is not an equilibrium state - nothing changes in time, but there is an energy flux flowing through the box. The statistical distribution in the box does not change in time and its entropy remains constant, but the overall entropy of the box plus its environment increases, since the whole is not in equilibrium (yet).
  • In situation B the energy of the box, in principle, may increase or decrease, depending on the molecules that are formed and broken (even if molecules are formed, this may result in energy release, if the molecules are more stable than composants). It is reasonable to think that in photosynthesis some energy is captured, so that it can be later released elsewhere in the plant, so the energy emitted is smaller than in case A.
  • Energy is a state function, but entropy is not. Thus, the fact that more energy is emitted does not guarantee that the entropy of the box is decreasing or increasing - it depends on the "path", i.e., on the specific processes happening.
  • Assuming that the photosynthesis results in a system becoming more ordered (more complex molecules are formed, although there may be also some molecules disintegrated), the entropy of the box decreases.

Thus, we have: $$ s_A=const\\ \frac{ds_B}{dt}<0 $$ If we could claim that the overall/global entropy changes in the same way, we would say that in case B the increase of the environmental entropy is greater. However, IMHO, we don't have enough information for making such a statement.

Roger V.
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