additions for clarity: I have a glass of ice (low physical entropy). I make a movie of the ice melting so that it takes one hour to melt completely. Then I keep the camera rolling for another hour at the glass of water. I compress them as mpegs and boom, the warm water by itself has higher averaged physical entropy over the duration of the movie, but very little information entropy and I wind up with a small file output. The first movie of the melting ice,with all of its nooks and crannies gradually shifting and reflecting as it melts, slides, and floats in the water = heavy mpeg file. Or you could run the movie backwards and make it seem like Shannon entropy is directly proportional to information energy…it doesn’t matter.
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