Sampling and statistical physics via symmetry

04/01/2021

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by   Steve Huntsman, et al.

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We formulate both Markov chain Monte Carlo (MCMC) sampling algorithms and basic statistical physics in terms of elementary symmetries. This perspective on sampling yields derivations of well-known MCMC algorithms and a new parallel algorithm that appears to converge more quickly than current state of the art methods. The symmetry perspective also yields a parsimonious framework for statistical physics and a practical approach to constructing meaningful notions of effective temperature and energy directly from time series data. We apply these latter ideas to Anosov systems.