I understand how TofE supports simple variation.
Here's my current understanding of TofE (and please correct me where I'm wrong):
Variations in DNA structure are what account for variations in the traits of animals. In other words, if a species of small black birds somehow becomes trapped in a very hot desert region, it may be likely that the species will adapt and change color over time in order to better survive the heat. I can understand how this could happen if there were variations in DNA structure from generation to generation causing changes in feather color.
Perhaps your problem in visualizing this is that you are unsure about the relationship of DNA to protein structure.
Do you understand how the DNA template (gene) is converted by RNA into a protein? Do you understand the role of amino acids in the formation of a protein?
When we speak of variations, we are speaking in essence of changing the function of a protein e.g. so that it no longer produces black pigment.
Now what structural change is required in the DNA to make the protein different, and why does this pose a problem as you see it?
In this scenario one cannot say that 2Lot should cause the species to die out because it is this very law that would be causing the variations to occur in the DNA. It's the thermodynamic entropy which is causing random changes through copy error in the variation of DNA information thus enabling selection of the fittest to occur.
No, the thermodynamic entropy is not causing random changes. Mutations are causing the changes.
What I do not understand is how this process can account for an increase in the complexity of DNA structure, if it does at all.
What do you mean by "more complex" DNA structure? As far as I know the only difference between one strand of DNA and another is that one may have more base nucleotides than another. But the overall structure of the molecule doesn't change.
Logically, the complexity of DNA structure unaided by some other process should break down over time.
I don't follow that line of logic. Can you spell it out for me? Why would a longer string of DNA necessarily have to become shorter over time?
So, this leads me to the following questions:
By what mechanism does DNA become more complex?
Well, this gets back to defining "more complex". If we know what you mean by "more complex" we might have some idea of why you see a problem here.
As far as I know DNA becomes more complex through mutations, in particular duplications and insertions. Both of these lengthen the strand of DNA and sometimes incorporate additional instructions into the coding or regulatory portion of DNA.
Is there some law of nature causing this to happen like 2Lot?
As far as I know it is whatever the causes of mutation are: sometimes via external agents such as radiation, sometimes simply through imperfect copying during reproduction. Nothing hugely mysterious or antagonistic to the 2LoT.
Is it a biological function within the cell? If so, is that function encoded within the DNA itself?
I think we have to get straight that mutations, other than those caused by external agents, are actually a breakdown in the copying mechanism. It is not a biological function to create errors in a copy of a DNA strand. So no encoding for mutations is required.
In fact, what is encoded in DNA and RNA is just the opposite: correcting mechanisms which check the accuracy of replication and keep mutations to a minimum.
Personally, I am inclined to think that if it were a cellular function like DNA replication, we would end up with wild mutations everywhere. So if TofE is true there must be some regulated process through which this happens.
We do get wild mutations, but most of them never see the light of day or have much effect on a species. There are two reasons for this. One are the self-correcting mechanisms mentioned above which prevent many errors in replication. The other is natural selection which limits the reproductive capacity of such wild variants that do occur.
Only variants which offer an adaptive advantage will be preserved by natural selection and bequeathed to the species as a whole.