From The Recursivity Blog:
Q1: Can information be created by gene duplication or polyploidy? More specifically, if x is a string of symbols, is it possible for xx to contain more information than x?
Q2: Can information be created by point mutations? More specifically, if xay is a string of symbols, is it possible that xby contains significantly more information? Here a, b are distinct symbols, and x, y are strings.
Q3: Can information be created by deletion? More specifically, if xyz is a string of symbols, is it possible that xz contains significantly more information?
Q4: Can information be created by random rearrangement? More specifically, if x is a string of symbols, is it possible that some permutation of x contains significantly more information?
Q5. Can information be created by recombination? More specifically, let x and y be strings of the same length, and let s(x, y) be any single string obtained by "shuffling" x and y together. Here I do not mean what is sometimes called "perfect shuffle", but rather a possibly imperfect shuffle where x and y both appear left-to-right in s(x, y) , but not necessarily contiguously. For example, a perfect shuffle of 0000 and 1111 gives 01010101, and one possible non-perfect shuffle of 0000 and 1111 is 01101100. Can an imperfect shuffle of two strings have more information than the sum of the information in each string?
The answer to each question is "yes".