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Common wisdom seems to suggest that living organisms have lower entropy that their environment. For example, the Wikipedia article on "Entropy and Life" mentions that Schrödinger thought that this was the case. On first thought this made sense to me; living organisms are more 'organized' than non-living matter. However, on closer inspection, I believe that this thought is completely wrong.

Although entropy is commonly linked with level of 'organization', a much more precise definition of entropy is a measure of how dispersed is the energy between the various possible energy modes of the molecules and atoms. In a living organism, the energy contained in its matter is highly distributed between many energy modes (translation, vibration, electricity, chemical, potential), while non-living matter this energy is more concentrated in less energy modes (mostly chemical).

As an example, my cat eats only dry cat food and water. Therefore the matter that composes my cat comes completely from the matter contained in the dry food, water and air. The energy in the food is concentrated mostly in chemical energy. However, the energy in my cat is more widely distributed between heat energy (which is really molecular kinetic energy), kinetic and potential energy as it runs around, electrical energy in its nervous system, and chemical energy in its fat and tissues. Clearly the energy is much more dispersed between different energy modes, meaning much higher entropy. Another way to see it, there is much more 'unknown information' about the microstates of the energy, given the macrostate of the energy contained in the cat, as opposed to the energy in the food. It is in this sense that we can say that the energy is more dispersed or 'disorganized' in the cat than in the cat food.

So any way I see it, it seems to me like living organisms are very efficient entropy producing machines. Not only do they increase entropy of their environment (closed system) but their internal entropy (open system) is also much higher.

So is the conventional wisdom wrong? Or am I wrong?

Thanks!

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  • $\begingroup$ Yet it takes very little configurational change to result in a dead cat - biological systems have less entropy than you seem to think. $\endgroup$ – Jon Custer Feb 25 '16 at 16:00
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    $\begingroup$ The way it's been explained to me is that living things are low entropy but 'make up' for that by constantly emitting high entropy infra red radiation. Living things are always at a temperature slightly above that of their surroundings. Until they die, that is... $\endgroup$ – Gert Feb 25 '16 at 16:05
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    $\begingroup$ How much entropy your body produces depends entirely on where you start counting the energy source, i.e. what's the highest temperature in your system is (is it the sun's surface temperature, its interior temperature, is it the temperature of the big bang?). It's not a function of your body but a function of your system boundary choices. As such the statement about entropy of living matter is essentially meaningless. $\endgroup$ – CuriousOne Feb 25 '16 at 20:44
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    $\begingroup$ Perhaps one way to think about it is looking at the Probability distributions, the various modes in which your cat's energy may be distributed are highly specific, with no real scope for them to be in any other state. So if you look at the probability distribution, you will expect a Dirac delta function corresponding to a particular mode. The distribution would not have any dispersion. The food, however, can be in various energy states (perhaps corresponding to a wide Gaussian), Hence looking at it from a broader scale, the possible Microstates for your cat are less than it's food. $\endgroup$ – Sreekar Voleti Jan 20 '17 at 4:24
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If we consider the body surface of the organism as the boundary of a system, then the organism as a machine tends to lower its internal entropy at the expense of raising entropy in the environment. To accomplish this great feat, the organism must have some means of absorbing energy from the environment - like the process of photosynthesis or feeding.

The clue, evidence that entropy is lowered? - just look at the amazing order, assembly of complexity, complex systems within the organism.

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  • $\begingroup$ My point is that being 'ordered, assembled, complex' does not necessarily mean lower entropy. I think it is just a common misconception to link entropy to 'order'. In reality, entropy strictly means how well spread out the energy is between possible energy modes, at the molecular and atomic level. It is only in this aspect that we can say that if the energy is concentrated in only one energy mode (e.g. molecular chemical energy) it is more 'organized' that if the energy were to spread to other modes as well ( e.g. molecular movement). This way, the cat has more entropy than the cat food. $\endgroup$ – user2028952 Feb 26 '16 at 16:02
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    $\begingroup$ @user2028952 the ordering business is a sloppy way of talking of statistical entropy: the number of microstates . A crystal, crustalizing out of a solution has lower entropy because of less microstates, at the expense of raising the entropy of the solution. Living organisms in a larger system have less microstates, because the DNA for example constrains the number of microstates from what the free atoms and molecules could attain. en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics) $\endgroup$ – anna v Jan 12 '18 at 18:19
  • $\begingroup$ This answer is essentially wrong since entropy is not related to "order", "organization" or "disorder". A refrigerator is an example of a system that reduces its entropy at the expense of the environment, and the key fact is that internal temperature is lower than the environment. A living body does not follow such behavior. If any, living bodies are usually hotter than the environment, meaning that entropy is even higher, as the OP states. The fact that order exists inside a living body does not mean that entropy has decreased. Physical order can increase while entropy is high. $\endgroup$ – RodolfoAP Dec 27 '18 at 22:23
  • $\begingroup$ As for a Boltzmann interpretation, a high entropy of a living body would correspond to a configuration with a low probability. A naive conclusion would be to state that a living entity corresponds to a molecular configuration with low probability, then entropy must be high. But such would be equivalent to say that a monkey cannot be formed by throwing a bunch of sand and expecting it to fall down to the ground as a monkey. The fact that we cannot create a monkey (by any technological means) does not imply that a molecular monkey configuration has a low probability and therefore entropy is low. $\endgroup$ – RodolfoAP Dec 27 '18 at 23:00
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It's not only the number of micro states, it is also the probability distribution of the micro states that matters. So your cat is more ordered, because its energy distribution is non-random but actually it is distributed in a very specific way. Most entropy is achieved when all the micro states are equiprobable. A cat is far from equilibrium, thus it's entropy is lower. This allows for the complexity of life.

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  • $\begingroup$ I can make the entropy of bacteria and even mammalian cells almost zero by freezing them near absolute zero. Then I can heat them up, again, and they will continue to live. This experiment renders your idea about life having any defined entropy meaningless. $\endgroup$ – CuriousOne Feb 25 '16 at 20:46
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    $\begingroup$ I do not see how that discredits my argument. What I meant was that for any system in general entropy can be reduced locally. Solar system, galaxy and so on. If the system is not in equilibrium it will have lower entropy. What I was trying to argue is that a cat is further from equilibrium. Not that there is a certain meaningful entropy of a cats life. $\endgroup$ – Ilya Lapan Feb 26 '16 at 0:51
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    $\begingroup$ It discredits the argument by pointing out that entropy is not a well defined or even useful quantity in this case. Use it for an ideal gas or use it on a black hole, where it does something for you. In case of life it does absolutely nothing useful. $\endgroup$ – CuriousOne Feb 26 '16 at 1:19
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    $\begingroup$ CuriousOne, I actually think that looking at entropy for life is an interesting approach that is worthwhile. Schrödinger for example discussed some of the ideas about entropy and what it implies about life in his book "What is life". Of course entropy of life in not defined. But life does work, produces heat, has temperature, life is a thermodynamical system so you can talk about entropy in its context. $\endgroup$ – Ilya Lapan Feb 26 '16 at 17:03
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    $\begingroup$ user2028952 I see your point. But I really think that microstates of cat food are actually more uniformly distributed than of a cat. Cat has energy stored in more different forms, correct, but that doesn't mean it has more microstates. Thinking of it similar to a molecule here which has rotational,translational and vibrational modes is not correct. In fact, cat tries really hard to stay in a set of specific microstates, if it ends up in a wrong state it could be dead. $\endgroup$ – Ilya Lapan Feb 26 '16 at 17:24
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If you look at entropy in its base system... lets say, without life whatsoever. This means only matter/energy in the system. Entropy increases over time. Right. Now as a simple example, lets say our system consists of a simple deck of cards, one card being shuffled randomly every day. Over time the cards will be perfectly random in the deck... this can represent our simple entropy in the system. Now, I check these cards every day after they have been shuffled, and the first time I check it they are all in order Ace to King: Clubs ,Spades, Diamonds, and Hearts following each other (like a new deck of cards). I say to myself that this is perfectly acceptable do to the laws of statistics... One possible outcome of many. But this is 52! (One HUGE number of combinations with only 52 pieces). Ok now every day as I check, my assumption about entropy increasing over time becomes true as the deck is shuffled more and more. But one day, I come back to the deck and I find it is like a new deck again... and the next day the same, and every day after that. Its like the shuffle is not working right. So I physically go into the system and shuffle them all myself -and now, I know they are all shuffled. But the next day I find that they are like a new deck again... and again... and again. So without a doubt from the systems point of view, I have to conclude that entropy decreases. What? How can this be? But it is true... the systems entropy decreases (How be it unnaturally). Right. I must either say that the 2nd law of thermal dynamics is not true, or that something unnatural is happening to the system. But I realize that just as I went unnaturally into the deck and shuffled it... maybe some thing else is later going into the deck and re-'organizing' it. But I still must conclude that for the 'local' natural system entropy decreases. But that's the whole point. LIFE goes against the natural laws of entropy of the 'natural' system by not as a simple factor of 52!, but rather 1Googleplex!. I exaggerate. But not really.

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You are right: strictly, living beings have a high entropy, perhaps higher than the environment. Pop wisdom about entropy in living beings is wrong, since entropy is not related to order. Entropy is just defined as a formula, which provides not enough elements for a conceptual interpretation. If any interpretation is possible, that is the one of classical thermodynamics: $$\Delta S = \sum_{i}\frac{(\Delta Q)_{i}}{T}$$

As I stated in two comments on this post:

... entropy is not related to "order", "organization" or "disorder". A refrigerator is an example of a system that reduces its entropy at the expense of the environment, and the key fact is that internal temperature is lower than the environment. A living body does not follow such behavior. If any, living bodies are usually hotter than the environment, meaning that entropy is even higher, as the OP states. The fact that order exists inside a living body does not mean that entropy has decreased. Physical order can increase while entropy is high.

... As for a Boltzmann interpretation, a high entropy of a living body would correspond to a configuration with a low probability. A naive conclusion would be to state that a living entity corresponds to a molecular configuration with low probability, then entropy must be low. But such would be equivalent to say that a monkey cannot be formed by throwing a bunch of sand and expecting it to fall down to the ground as a monkey. ...

The fact that we cannot create a monkey (by any technological means) does not imply that the molecular configuration of a monkey has a low probability and therefore the entropy of monkeys is low.

The perception of probability in this case is highly subjective since we don't know what is the chain of processes that end up in the molecular configuration that we call a living monkey.

A living being has a low entropy only under a large set of subjective assumptions, which carefully examined will always prove to be false. The only real fact is that monkeys exist due to spontaneous evolution of this system we call nature.

Moreover, high entropy means that interactions between subsystems are at its maximum, which corresponds better to the definition of a living being. When two gases at different temperatures mix, entropy grows, but that doesn't mean that energy has stopped flowing. Energy is flowing at its best throughout all the molecules. The same happens with living beings: at high entropy, more interactions exist. That fits better the definition of a living being: high entropy and a high level of interaction between subsystems.

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