Sampling and statistical physics via symmetry

DOI10.1007/978-3-030-77957-3_20arXiv2104.00753MaRDI QIDQ6364370

Publication date: 1 April 2021

Abstract: 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.

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Quantum equilibrium statistical mechanics (general) (82B10) Monte Carlo methods applied to problems in statistical mechanics (82M31)

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