Computation that computes

While I was recently browsing the web for interesting physics papers, I came across one in Nature titled ‘A thermodynamically favoured molecular computer’. The work itself seemed interesting but what caught my eye was a pair of lines in the abstract: “… computation can be embedded in a system relaxing to a thermodynamically favoured equilibrium state. Machine learning and search algorithms use this idea, although executed on non-equilibrium architectures at enormous energy cost.” I have come across versions of this statement when writing about the connections between machine learning and statistical physics — a feat the Nobel Prize for physics recognised in 2024. But then I thought that in the spirit of really learning how this was and to have some reference text I could come back to, I should write about it. So here goes. The central idea seems to be something physicists and computer scientists are very familiar with but which nonetheless landed, to me, as a wonderful surprise when I…