Thermodynamics of DNA double helix formation?
The entropy of a system decreases when 2 single stranded DNA molecules come together and form a double stranded molecule.


Are you sure?

I would argue that association of two single-stranded DNA strands to form a double-strand is energetically favourable — for entropic reasons. This should be a combination of


the hydrophobic effect
the liberation of a few water molecules per base that are no longer needed in hydrogen bonding.


Point 2 is explained quickly. Upon association of two single strands, the characteristic Watson-Crick base pairs form and hydrogen bonds are established between the DNA bases. These hydrogen-bond donors and acceptors were previously associated with water molecules keeping them close to the DNA single strands and thus rather ordered. These water molecules are now liberated; and since there are at least two per base, this partial process is entropically favourable.

Point 1 may not be as clear as point 2, but it again boils down to the fact that water molecules are liberated from a rather well-defined structure. Large parts of DNA — the area around the bases — are not as hydrophilic as other parts of the molecule or water itself. While they still are somewhat polar, their interaction with water is not ideal. Thus, the ‘surface’ water molecules will form a kind of defined boundary around the molecule. This boundary becomes lesser overall if the surface to volume ratio decreases. And upon association, you have almost double the volume in practically the same surface (i.e. you have halfed your effective surface). Therefore again, a large number of water molecules are liberated.

If DNA association is entropically favoured, there is no need to invoke any heat.