Before going any further I recommend you read Schrödinger's book  WHAT IS LIFE. He addresses the thermodynamic question and shows that living systems beat the law of averages in non random processes. Thermodynamics usually describes random processes. Schrödinger presented an explanation of entropy as it applies to living creatures based on the third law of Thermodynamics governing non random processes.

S = k Ln ( D)    where D represents possible energy states randomly filled

and

S = - k Ln (1/D)  where D represents possible energy states prevented from being randomly filled. Combining two equations and with subscripts added the entropy is regulated by the ratio of random and non random energy states.

S = k Ln (Dr/Dn)

Then in non reversible processes the second law of thermodynamics is not strictly  applied if the system contains a substantial number of biased decisions like DNA, RNA, and enzymes acting selectivity.

The same principle can be applied in an electric circuit containing diodes. A small Dark Current flows even when the power supply is disconnected. It is too small to be of much practical use, but large enough to cause design problems in digital cameras and televisions. The dark current represents a decrease of entropy in biased diodes as described in the equations, but Is not in violation of the Second Law since the current flow is not reversible.

Schrödinger gave similar explanations for the success rate of biological replication far more accurate than the Thermodynamic predicted n(1/2) error rate.

In reply to the question of free will, about 6 years ago Ulla Mattfolk a biologist in Finland and I collaborated on a proof of free will based on the decoherence of entangled wave functions of Quantum Mechanics. In other words, a region of the universe has a limited capacity for storage of information that can be used in making choices, but the number of possible questions and choices in that region is not limited. Another explanation is that Uncertainty Principle allows us to exercise free will at least part of the time, by applying non random answers to questions. An equally valid proof is found in Shakespeare plays, where people are held responsible for actions, even if they feel powerless to stop, and the witches foretold it. 

Where to step in? Schrödinger's book is old and lacking a lot of data, also qualitative instead of quantitative. Shakespeare plays are fiction. Maybe you can build a non fiction version.

Depends on your definition of life, and oddly enough it depends whether you have free will or not, see e.g. the analysis at 

https://www.researchgate.net/publication/301712130_Immanence_or_Transcendence_A_Mathematical_View

Conference Paper Immanence or Transcendence? A Mathematical View

Peter,

my advice would be to study Biochemistry with its manifold of well understood processes of self-organisations and to free yourself from the simple-minded attitude of many physics books on thermodynamics and statistical mechanics who end their understanding with homogeneous systems.

A second marvellous  source of inspiration and insight is the programming of  model systems and running simulations with them.

Before going any further I recommend you read Schrödinger's book  WHAT IS LIFE. He addresses the thermodynamic question and shows that living systems beat the law of averages in non random processes. Thermodynamics usually describes random processes. Schrödinger presented an explanation of entropy as it applies to living creatures based on the third law of Thermodynamics governing non random processes.

S = k Ln ( D)    where D represents possible energy states randomly filled

and

S = - k Ln (1/D)  where D represents possible energy states prevented from being randomly filled. Combining two equations and with subscripts added the entropy is regulated by the ratio of random and non random energy states.

S = k Ln (Dr/Dn)

Then in non reversible processes the second law of thermodynamics is not strictly  applied if the system contains a substantial number of biased decisions like DNA, RNA, and enzymes acting selectivity.

The same principle can be applied in an electric circuit containing diodes. A small Dark Current flows even when the power supply is disconnected. It is too small to be of much practical use, but large enough to cause design problems in digital cameras and televisions. The dark current represents a decrease of entropy in biased diodes as described in the equations, but Is not in violation of the Second Law since the current flow is not reversible.

Schrödinger gave similar explanations for the success rate of biological replication far more accurate than the Thermodynamic predicted n(1/2) error rate.

In reply to the question of free will, about 6 years ago Ulla Mattfolk a biologist in Finland and I collaborated on a proof of free will based on the decoherence of entangled wave functions of Quantum Mechanics. In other words, a region of the universe has a limited capacity for storage of information that can be used in making choices, but the number of possible questions and choices in that region is not limited. Another explanation is that Uncertainty Principle allows us to exercise free will at least part of the time, by applying non random answers to questions. An equally valid proof is found in Shakespeare plays, where people are held responsible for actions, even if they feel powerless to stop, and the witches foretold it. 

Where to step in? Schrödinger's book is old and lacking a lot of data, also qualitative instead of quantitative. Shakespeare plays are fiction. Maybe you can build a non fiction version.

I read an article where it was shown convincingly, that "life" is the ultimate form of entropy reduction. It implied that life is as much a natural result of thermodynamic processes, as are crystals. DNA replicates for the same reason crystals do. Life, breathing air, eating food and radiating heat increases entropy, while the living organism becomes better organized and "thinks", putting random electrical signals into ordered patterns. This is the ultimate reduction of entropy within the living system.

I don't recall, but it was a magazine not a journal. So Science News, or Scientific America, something like that...

Dear Filippo, thank you - this is really very interesting!

So if we could code these fluctuations to be an evolutionary DNA sequence of the Universe, some special series of codes would also be a word meaning life and us. And who knows maybe all these are just not yet recognized in the endless number pi precision series (just kidding). But indeed I like your explanation a lot.

^ totally agree, actually I think my latest comment was a jokingly/figuratively association what guys you mentioned may interpret from there, and from your reaction I see I was not so much wrong. After all, in a large stochastic series of random noise chances are big to find _any_ message in _any_ language, and WE are those who decide that a piece of data makes an piece of information. Another interesting discussion but leads away from this thread towards semiotics.