But of course information can increase over time. I'll point again to evolutionary computation. Evolution explains this by reference to random mutations.
You can see this for yourself with some pretty simple code. Assume that fitness is defined as similarity to the vector [1 2 3 4 5 6 7 8 9 10]. Start from the vector [0 0 0 0 0 0 0 0 0 0]. Now copy it three times, with each entry of each copy having a 5% chance of changing in value (to something random between 0 and 10). Then save the copy with the most entries in common with our fitness vector. Repeat the process. Eventually you'll have [1 2 3 4 5 6 7 8 9 10]. If you want a more robust test, save the copy which gives the lowest value of the sum of the absolute values of the difference between each entry in V and F. There you go - you've created information. Now, we began by knowing what was most fit, but nature works that way too - there is a definite standard for fitness that mutations are kept or discarded based upon. This is what natural selection does.
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