What are the arguments towards the Life-and-Entropy relation? I've heard it from a few people, and I've seen it popup here in the site a couple of times. There seems to be speculation (and studies?) towards this idea, and this is what I've picked up so far:


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*Living organisms are low entropy systems.

*The second law of thermodynamics is somehow strongly connected to the origin of life itself.


This is a very interesting idea, unfortunately I've never seen anyone elaborate beyond that. I'd like to understand it a little better. Specifically:


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*Why are the above statements true (neither is immediately obvious to me)?

*And what are the other arguments in favor of this theory?


I'll accept both answers for and against this point of view, as long as it reasonably justifies why the above statements are correct/false.
Note: I believe the thermodynamic definition of entropy is the one commonly used with these arguments. And I'm not sure what definition they use for life. The Wikipedia page is pretty vague on this.
 A: The first point is simple to address. Gas that is located in the corner of the room has lower entropy than gas that is scattered all over the room because it has smaller number of accessible microstates that correspond to it. Similarly, you can consider one concrete organism that has very ordered structure. Most of the atoms just need to be where they need to be, otherwise you'd die; of course there is still variability explaining the diversity of the species, but that diversity doesn't extend all the way to your molecules flying around as a gas. So life is in a hypothetical small corner of the room representing every possible ordering of atoms.
There is also a notion that living organisms lower the entropy of their surroundings. This is indeed correct. Again, every ordered system must have lower entropy than unordered system (because it has lower number of accessible microstates) and so if you convert the heap of mud into a house, you'll lower entropy of your immediate surroundings. But in the process of ordering you'll exert great amount of work and heat and increase the total entropy of the universe.
As for the origin of life, I am not sure about the connection with second law. To me it's just a question of probability. If anything it seems to be an application of Poincaré recurrence theorem (which actually denies second law, or more precisely sets it out as only a statistical statement that is eventually bound to fail). Let's say proto-life is defined as certain small molecules that start to exhibit some signs of life (reproduction? self-correction? having certain metabolic processes? I'll leave that to experts on life). These are still complex ordered systems and so improbable to form, but the oceanic waters of the young Earth were probably big enough such that number of microscopic disordered systems was comparable with recurrence time associated to them. Poincaré recurrence theorem then says that in finite time those unordered systems will assemble themselves into ordered systems.

Note: so why don't we see broken eggs assembling into original unbroken eggs? Answer: because it would take time $t \sim \exp({\Delta S \over k})$. So if you have enough time (or equivalently enough eggs), you'll see it assembled. Problem is these times are huge for macroscopic objects. But for proto-objects that started the evolution of life, that time should be reasonably small (like few hundreds of millions of years).
A: 
Living organisms are low entropy systems.

Clearly the energy coming from the Sun is what powers life on Earth. While there are some microorganisms that use geothermal energy, this is true for the large majority of life.
The Earth's energy budget is quite well understood, with the Sun pouring $174\times 10^{15} W$ worth of energy in it, and the Earth re-radiating all of it (assuming thermal equilibrium) through reflection (30%), radiation from the clouds (64%) and radiation from the ground (6%).
So, since the energy coming from the Sun is also going out at the same rate, where does all energy that life needs comes from?
It can be traced back through the food chain to photosynthesis, which creates more complex and energetic molecules and generates waste heat (blackbody radiation). While the overall entropy balance is positive, photosynthesis decreases the plant's entropy while increasing the environment entropy.
So your statement needs to be understood in this context: what powers life is not the energy of the Sun, but the fact that this energy has a low enough entropy that Earth can radiate the energy back via black body radiation while decreasing entropy locally.

The second law of thermodynamics is somehow strongly connected to the origin of life itself.

The only thing I can think of around this statement is that some creationists have tried to argue against abiogenesis on the basis of the law of entropy - in the sense that complex, ordered systems like living beings have a lower entropy than a dead system with the same atoms without structure. Which is true - and the explanation of why abiogenesis does not necessarily violate the law of entropy is in my considerations above.
A: Entropy and the Second Law of Thermodynamics relate to life because life is made possible by the flows of energy implicit in the second law and the selective storage and manipulation of the biochemistry made possible by those flows.

Living organisms are low entropy
  systems.

In classical thermodynamics, entropy is a measure of the thermodynamic energy availability of a system. Thus a low entropy system has energy available in a form that may be used to perform work while a high entropy system has relatively less energy available. Alternately, entropy can be seen as a measure of disorder where low entropy means a relatively ordered system and high entropy means a disordered system. Finally, in statistical mechanics, entropy can also refer to information content where low entropy means relatively higher information content than high entropy.
Living organisms are low entropy by all three related measures. The more complex the organism, the more true this statement is. Live organisms store energy and make it available for metabolic processes to move, eat, think, etc. Organisms are highly ordered systems, the most complex systems we have seen in the universe thus far. Organisms also have very high information content. Organic systems are controlled through a complex intermix of chemical, electrical, and genetic information that we do not even fully comprehend at this point, even for the most basic single celled organisms. They are the most highly ordered systems known.

The second law of thermodynamics is
  somehow strongly connected to the
  origin of life itself.

The second law of thermodynamics states that in a closed system, entropy will tend to increase and that entropy will flow from the low entropy region to the high entropy region. This relates to life in two specific ways:


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*It makes life less likely, in general, since life must originate through a random fluctuation to a low entropy state. Since entropy normally increases, over time the entropy of the system will be higher and therefore less likely to originate life.

*It makes life more likely on a planet like Earth that sits in the middle of the entropic gradient of the entropy flows from the very low entropy Sun outward to the relatively higher entropy solar system. The surface of the ocean is the edge of a very steep thermodynamic gradient where the energy from the sun mixes with the relatively cool water of the ocean. In these gradients, it is much more likely for random fluctuations to result in a very low entropy molecule like an amino acid or eventually DNA because there is a continuous energy flow from the Sun through the gradient. This energy makes possible various endothermic chemical reactions, increases the rate of chemical reaction, and offers a source of energy for continued conversion for metabolic purposes for any living organisms.
So both statements are true.
A: In the days since Boltzmann and Clausius our understanding of systems far from equilibrium has increased drastically. Developments in the past two decades have also shown that the 2nd law - as it was classically understood - was not the be all and end all when it came to understanding the emergence of complex systems such as those of life.
A good place to learn about these discoveries is with the Fluctuation Theorem which was first proposed in 1993 by Denis Evans, Cohen and Morriss. To quote from the abstract of the Wikipedia article:

While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously decrease; the fluctuation theorem precisely quantifies this probability.

(emph. mine). Ultimately all the systems of life exploit this weakness of the 2nd law - that it is a statistical statement and not a microscopic law. What these Fluctuation theorems have demonstrated that given the right conditions an isolated system can exploit the possibility that its "entropy might spontaneously decrease". In order to be able to exploit this possibility the system in question must be comparable in size to the thermal fluctuations in its environment. This is true for all biological motors such as those responsible for energy production via ATP, myosin motors which control muscle movement and artificially manufactured nano-machines.
Apart from these considerations, there is also the fact that life-bearing systems are always far from equilibrium. When, for instance, "Creationists" try to use the 2nd law as an argument for, well, "creation" they forget that we live in the presence of a star which constantly supplies the earth with energy resulting in the planet being far from thermal equilibrium on a macroscopic scale so that no application of the 2nd law in its traditional form - i.e. without taking into account the Fluctuation Theorem - is possible.
Summary: If we want to even begin to speak sensibly of such questions we have to understand the statistical mechanics of non-equilibrium systems, which we have only just begun to do.
