Here is a recent paper:
[Carbon release by off-axis magmatism in a young sedimented spreading centre](http://www.nature.com/ngeo/journal/v4/n1/abs/ngeo1006.html)
>Continental rifting creates narrow ocean basins, where coastal ocean upwelling results in high biological productivity and organic-rich sedimentation. In addition, topographic gradients promote silicate weathering, which consumes atmospheric CO2 (ref. 1). The carbon flux associated with these processes has led to the suggestion that rifting may cool the atmosphere, leading in some cases to glaciation2 and even a snowball Earth scenario3
I will dig up the data from Prof. Lizarralde and their findings and possible models for the warming or cooling, great activity for migrained insomnia. Again I do not see the role of sun in this.
While I believe the sun has a lot to do with the entropy or complexity of our planet, I also believe that our water systems are also contributing, my intuition tells me even more that sun but this is not an inference.
Moreover in other papers they are talking about the salinity of the water in relation to entropy :
[Climatological mean distribution of specific entropy in the oceans](http://www.ocean-sci-discuss.net/4/129/2007/osd-4-129-2007.pdf)
>Entropy, as enthalpy, internal energy of seawater is scientifically interesting thermodynamic state function of seawater.
It seems they use Entropy and Enthalpy as same definition for disorder.
Salinity of the ocean waters play important role in the derivative equation for the entropy!