At this point, people often argue over the rule's scope. Claims are made that the Earth is not a "closed system" and that the rule only applies to closed systems. This paper attempts to prove that argument invalid by demonstrating the math is the same for open systems as well.
The math isn't the same for open systems. Open systems are extraordinarily different from closed systems. All physicists know this. Moreover, the behavior of open systems has been studied quite a bit.
Trouble is that, as a universe, perfect disorder would also violate the second law of thermodynamics. It would, in effect, be its own form of order.
In reply to the OP, this paper fails to pass common sense from the abstract. Take the last sentence of the abstract and argue:
"Thus, unless we are willing to argue that the influx of solar energy, water and nutrients into the acorn makes the appearance of trees not extremely improbable, we have to conclude that the second law has in fact been violated here."
The conclusion is stupid. There are numerous processes where entropy decreases locally - many have nothing to do with biology at all. So either the details are incorrect or the assumptions are incorrect.
In this case, the details of the paper are extremely incorrect:
Equation 1 is wrong: There should be a flux integral, not a divergence. Something like the followinghttp://en.wikipedia.org/wiki/Thermal_conduction#Integral_formhttp://en.wikipedia.org/wiki/Flux#Flux_definition_and_theorems_2
Equation 3 is wrong: (i) Terms are missing from differentiation. (ii) Entropy is not a state variable and cannot be integrated without supplying a thermodynamic process. (iii) The very language "distribution of heat" also betrays a lack of understanding. There is no such thing in this context. (iv) The integral is incorrect in several different ways. (v) The units are incorrect.
I'm not going to read any further. The author is an idiot, has no understanding of thermodynamics (even for closed systems), cannot perform basic calculus operations, cannot produce equations with correct units (high-school level physics), and cannot think logically.