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What plausible things might happen in a *mildly* negative-entropic environment?

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Entropy in a casual definition is the tendency of things to progress from order to disorder. There are a variety of specific definitions in different arenas of thought. For example, heat will diffuse from one side of a room to another until the entire room is roughly the same temperature. In thermodynamics then, entropy is the tendency to minimize the variation in heat energy throughout a medium. Other disciplines have their own meaning. In biology entropy might refer to the destruction of complex structures. In cosmology it might be defined to be a part of any process that is irreversible (like matter falling into a black hole). What happens when this natural entropic process is reversed, just slightly?

Unfortunately, the general concept of entropy is not always well defined in a technical sense, but it has captured the imagination of many scientists and natural philosophers.

I am thinking about a region of anti-entropy (or negative-entropy, if you prefer) which is a place where there is a tendency of things to progress from disorder to order. There are many interpretations of what it would mean if we lived in a strongly anti-entropic world, but these interpretations are typically tied to a specific technical concept that ends up being difficult to use in a worldbuilding context.

One classic interpretation of anti-entropy under the order/disorder paradigm would be a shattered vase spontaneously reforming itself, or a spilled mug of coffee spontaneously reforming and up-righting itself. If entropy is the spontaneous creation of disorder, then anti-entropy is the spontaneous creation of order. In the cosmology context we can imagine reversing an irreversible process. If you were to reverse the black hole process, you would see matter, energy, or even complex structures like space ships spontaneously generate and fling themselves away from their origin (AKA a "white hole"). Anti-entropic behavior under the thermodynamic concept would be spontaneous concentration of heat energy. These are neat concepts, but they're such strong strong interpretations that they would disrupt our normal understanding of life.

We never expect a broken vase to spontaneously un-shatter itself, and the inhabitants of this anti-entropic field would not either. Nor would they expect light and matter to spontaneously generate, etc. However, there is a minor tendency towards ordering the world rather than disordering. They might count on the fact that cracks in ceramics slowly fix themselves. Refrigerators are a little more efficient because thermal insulation just works a bit better. Dust might tend to clump together in corners. Kicking a pile of gravel would tend to result in a few odd stacks of pebbles.

  1. What kinds physics would be fudged just a little bit such that our world would look basically the same, but anti-entropic phenomena would occur?
  2. What kinds of phenomena would be intuitive to an inhabitant of a slightly anti-entropic environment?
  3. Would any major physical processes necessary for life be majorly affected?
  4. It might be necessary to say that small-scale local phenomena are allowed to be anti-entropic, but large scale phenomena are required to behave as normal. Could those two things be reconciled?

I'm thinking more qualitatively than hard-science answers, but those are certainly welcome. I'm also not limiting myself to the fields of science I've discussed, those are just the ones I'm more familiar with.

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The second law of thermodynamics states that global entropy of an isolated system always increases or remains constant

This tells us a couple of things that are relevant here:

  • If the system is not interacting with anything, entropy cannot decrease. I.e. the entropy of the universe will never decrease without violating the laws of physics as they are currently known
  • If you have a sub-system of the above isolated system, the entropy of the sub-system can decrease. However, this causes entropy somewhere else to increase so that the total change is either positive or $0$

A simple example of a decrease in entropy of a sub-system is taking some water vapour and cooling it down to become liquid - you've taken heat out of a system. This heat has gone somewhere else and increased entropy there, but the entropy of the water vapour has decreased. A fridge is a good example of a physical object that can cause this to happen.

A white hole is different, as it (I think) decreases the entropy of the universe, so invalidates the second law of thermodynamics and so are assumed to not exist because:

"The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations"”then so much the worse for Maxwell's equations. If it is found to be contradicted by observation"”well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics, I can give you no hope; there is nothing for it but to collapse in deepest humiliation." Sir Arthur Eddington (The Nature of the Physical World, 1915)

In other words, anything that increases order in any way gives a decrease of entropy of whatever is becoming increasingly ordered, but at the cost of increasing the entropy somewhere else.

So to answer all your other questions: We already live a world where entropy of small regions can decrease!

Interesting aside: It is possible for a "broken vase to spontaneously un-shatter itself", it's just that the probability of such an event occurring is so small that you would have to wait longer than the age of the universe for it to have any reasonable probability of occurring

Edit: I've re-read the question and feel that I should add the below: Things like kicking a pile of gravel and the result being smaller piles of pebbles is 'impossible' due to probability, not entropy. That is, as per 'interesting aside', it's perfectly possible for such a thing to happen, it's just that the probability of it happening is tiny when compared with the probability of it not happening. Saying that an isolated system tends towards maximum entropy is essentially the same as saying that the system tends towards the most likely outcome, because they are the same thing. The above quote from Eddington is true, not because of physics, but because a system increasing in entropy is a system tending towards the most likely outcomes, which is unavoidable by definition. So, if you want to decrease the entropy of something, you can do it easily (e.g. pour boiling water into a mug, then put it in the fridge). If you want an area where this happens by itself, then you need to either travel backwards in time, a white hole or something similar, which is all assumed to be impossible (to current knowledge) because they violate the second law of thermodynamics. Quantum physics does however do weird things with probabilities (see e.g. the Wigner function), so who knows what's actually possible on the tiniest of scales? Using quantum physics to decrease entropy of a subsystem is entirely possible - http://www.nature.com/nature/journal/v474/n7349/full/nature10123.html - but again, the 2nd law of thermodynamics isn't broken.

To sum up, entropy is probabilistic by definition, so things like vases fixing themselves doesn't happen, not because of physics, but because of probability. However, decreasing entropy of a subsystem (at the expense of increasing entropy somewhere else) is an everyday occurrence.

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