That's a great question! I should start by clarifying that I was using order in this post in the sense of "following predictable rules", intended to be the opposite of chaos. The air in a room is ordered in this sense; it acts predictably by spreading out to fill space and equalise pressure differences. This predictability is necessary for life, but it does not fully encapsulate life itself. Life has a deeper kind of order that is characterised by organisation and structure beyond what occurs randomly.
It is this deeper kind of order that is characterised by Schrodinger's concept of negentropy. Specifically, negentropy is a measure of how much a system's entropy is less than its maximal possible entropy. As a starting point, a significant negentropy, therefore, requires having a large maximal possible entropy, which is only possible for large systems. Small systems have low entropy, but also have low negentropy; they are, in a word, simple. So massive combinations of entropic entities are a necessary precondition for negentropy.
Once you have such large, highly entropic systems, negentropy is achieved by lowering the entropy in a durable way. Because high entropy is only a statistical tendency, small levels of negentropy are constantly occuring spontaneously. Usually this is quickly undone since the system tends back to maximal entropy. However, certain configurations can be "metastable" because there is some barrier to their destruction that takes a long time to overcome. For example, atoms may be structured into complex molecules that would require a significant initial input of energy to break apart. At the most abstract level, evolution by natural selection is the process by which these metastable instances of negentropy accumulate over time to give rise to organisms with much lower than maximal entropy.
So natural selection is the additional ingredient necessary for negentropy, beyond the statistical effects that give rise to predictability which I discussed in this post.
Thanks Paul, for that great reply and hope you are having a good break. If you have time, your reply has generated two questions for me:
1. Could it be said that a “barrier to destruction” (as above) is an inverse way of saying a “support for selection”, as in evolutionary theory. Meaning that the same algorithm of random mutation + selection underlines order all the way down and up?
2. Can we talk meaningfully about entropy at the level of the “quantum vacuum”, and if so is it quantifiable?
1. Yes, absolutely. Fundamentally, the configurations we observe in the universe are there because they satisfy (at least) one of two selection rules: either their formation is likely, or they persist for a long time once they are formed. The best way for a configuration to keep persisting for a very long time is for it to make many copies of itself, so that even if the original is destroyed, the configuration will still continue in the form of the copies. This process of replication is what life does, and what makes it special. It allows for the persistence of DNA across billions of years, and allows for otherwise very unlikely configurations to exist in nature, which can in turn become the basis for new configurations through mutation. But as you say, all of this is just one example of the general rules: things exist either because their formation is likely, or because they persist for a long time once formed.
2. This question stretches my knowledge of quantum field theory a bit. A classical vacuum has no entropy, because we cannot arrange "nothing" in multiple different ways. Another way to say this is that the classical vacuum state is unique. My understanding is that the quantum vacuum is similarly a unique quantum state, just a more complicated state than the classical vacuum state. If I am correct about that, then it would also have no entropy. It is true that when the quantum vacuum state is interacted with other matter, there are multiple possibilities that could occur corresponding to the range of possible quantum fluctuations. But I understand these multiple possibilities to only arise as a result of the interactions, and so I assume the entropy that corresponds to such possibilities to have been introduced by the interacting matter and not to have already been present in the vacuum.
Thanks Paul, appreciate your responses. Of course, once you have done so further thoughts and questions expand exponentially, but I will desist and wade in on one of your later posts.
So how or why is it the neg-entropy (order) emerges from massive combinations of entropy?
That's a great question! I should start by clarifying that I was using order in this post in the sense of "following predictable rules", intended to be the opposite of chaos. The air in a room is ordered in this sense; it acts predictably by spreading out to fill space and equalise pressure differences. This predictability is necessary for life, but it does not fully encapsulate life itself. Life has a deeper kind of order that is characterised by organisation and structure beyond what occurs randomly.
It is this deeper kind of order that is characterised by Schrodinger's concept of negentropy. Specifically, negentropy is a measure of how much a system's entropy is less than its maximal possible entropy. As a starting point, a significant negentropy, therefore, requires having a large maximal possible entropy, which is only possible for large systems. Small systems have low entropy, but also have low negentropy; they are, in a word, simple. So massive combinations of entropic entities are a necessary precondition for negentropy.
Once you have such large, highly entropic systems, negentropy is achieved by lowering the entropy in a durable way. Because high entropy is only a statistical tendency, small levels of negentropy are constantly occuring spontaneously. Usually this is quickly undone since the system tends back to maximal entropy. However, certain configurations can be "metastable" because there is some barrier to their destruction that takes a long time to overcome. For example, atoms may be structured into complex molecules that would require a significant initial input of energy to break apart. At the most abstract level, evolution by natural selection is the process by which these metastable instances of negentropy accumulate over time to give rise to organisms with much lower than maximal entropy.
So natural selection is the additional ingredient necessary for negentropy, beyond the statistical effects that give rise to predictability which I discussed in this post.
Thanks Paul, for that great reply and hope you are having a good break. If you have time, your reply has generated two questions for me:
1. Could it be said that a “barrier to destruction” (as above) is an inverse way of saying a “support for selection”, as in evolutionary theory. Meaning that the same algorithm of random mutation + selection underlines order all the way down and up?
2. Can we talk meaningfully about entropy at the level of the “quantum vacuum”, and if so is it quantifiable?
Thank you, and sorry for the late reply!
1. Yes, absolutely. Fundamentally, the configurations we observe in the universe are there because they satisfy (at least) one of two selection rules: either their formation is likely, or they persist for a long time once they are formed. The best way for a configuration to keep persisting for a very long time is for it to make many copies of itself, so that even if the original is destroyed, the configuration will still continue in the form of the copies. This process of replication is what life does, and what makes it special. It allows for the persistence of DNA across billions of years, and allows for otherwise very unlikely configurations to exist in nature, which can in turn become the basis for new configurations through mutation. But as you say, all of this is just one example of the general rules: things exist either because their formation is likely, or because they persist for a long time once formed.
2. This question stretches my knowledge of quantum field theory a bit. A classical vacuum has no entropy, because we cannot arrange "nothing" in multiple different ways. Another way to say this is that the classical vacuum state is unique. My understanding is that the quantum vacuum is similarly a unique quantum state, just a more complicated state than the classical vacuum state. If I am correct about that, then it would also have no entropy. It is true that when the quantum vacuum state is interacted with other matter, there are multiple possibilities that could occur corresponding to the range of possible quantum fluctuations. But I understand these multiple possibilities to only arise as a result of the interactions, and so I assume the entropy that corresponds to such possibilities to have been introduced by the interacting matter and not to have already been present in the vacuum.
Thanks Paul, appreciate your responses. Of course, once you have done so further thoughts and questions expand exponentially, but I will desist and wade in on one of your later posts.