Entropy is loosely defined as "disorder." Therefore, anything that results in more order is ostensibly decreasing entropy.
Thus, the spontaneous ordering of atoms into crystals and aggregation of atoms into organic molecules have been touted as being contrary to the second law.
No . The 2nd law defines which directiion a process is likely to proceed. If you postualte a process for which the 1st law holds, but the energy is being tranferred in the wrong direection ( based on 2nd law ) then you have your hypothetical scenario.
For example, the radiator on your car is hotter than ambient air temp, and the first law says the energy lost form one body ( radiator) equals the heat gained by the other body ( ambient). The 2nd law says the heat goes from the hot body (radiator) to the cold body (ambient). But you can pretend the opposite direction of heat flow, from ambient to radiator, meet the 1st law, and violate the 2nd law.
Draw the dotted line around a system which is less than the universe and you can see imaginary violations of the 2nd law all the time. But the entropy of the UNIVERSE increases for all irreversible processes, and is zero only for reversible processes. That includes the creation of new molecules, crystalization etc.
The construction of a skyscraper from materials originally dispersed over Earth, the ordered symbols on a printed page, the growth of a living thing from a random mix of molecules, the fractionation of compounds by distillation, or by crystallization, are all examples in which entropy decreases.
However, all those examples do not involve "closed" systems. The entropy decrease associated with those processes is more than balanced by the entropy increase elsewhere in the universe as moltenmetal says.
We cannnot escape the second law of thermodynamics.
Therefore violating it is just a creature of the imagination.
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