If we take a description of the solar system in terms of Newton's equations then the solutions are time-reversible.

But many phenomena in nature are observed to be non-reversible, "dissipative", hence not having time-reversible solutions. For instance, a glass falling off the table and breaking.

The big question is: can the second law of thermodynamics be deduced from the fundamental differential equations of physics ?

Or more generally are there differential equations whose solutions are mostly entropy-increasing ?

On the other hand can we find (a system of) differential equations whose solutions are generally entropy-decreasing ? Or in which entropy-decreasing phenomena occur in relatively frequent bursts ? Differential equations which would have solutions in which the pieces spontaneously assemble into the glass on the table ?

Contemporary physics is essentially incomplete (cf. the need for dark matter, dark energy, extra dimensions, etc.). Perhaps in the complete picture entropy is actually strictly conserved. The entropy-increasing forces/fields are counterbalanced by (at present unknown) entropy-decreasing ones, in which entropy-decreasing phenomena occur in relatively frequent bursts.

Then it is this entropy-decreasing aspect of nature that is the main cause of life, the cause of the relatively frequent bursts of increased self-organisation and complexity (which would then be further modulated (or "selected") by the constraints of the environment and the ecosystem).

Perhaps the "collapse of the wave-function" could be approached thermodynamically as well ?

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