Werner Krauth (ENS, Paris) was in Dauphine today to present his papers on irreversible Markov chains at the probability seminar. He went back to the 1953 Metropolis et al. paper. And mentioned a 1962 paper I had never heard of by Alder and Wainwright demonstrating phase transition can occur, via simulation. The whole talk was about simulating the stationary distribution of a large number of hard spheres on a one-dimensional ring, which made it hard for me to understand. (Maybe the triathlon before did not help.) And even to realise a part was about PDMPs… His slides included this interesting entry on factorised MCMC which reminded me of delayed acceptance and thinning and prefetching. Plus a notion of lifted Metropolis that could have applications in a general setting, if it differs from delayed rejection.