Sampling and statistical physics via symmetry
arXiv:2104.00753 · doi:10.1007/978-3-030-77957-3_20
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.
Proceedings of Les Houches 2020 school on Joint Structures and Common Foundations of Statistical Physics, Information Geometry and Inference for Learning
References in corpus (9)
- Negative Absolute Temperature for Motional Degrees of Freedom
- Temperature in and out of equilibrium: a review of concepts, tools and attempts
- Markov Chain Monte Carlo Method without Detailed Balance
- Efficient computation of the Zassenhaus formula
- Gibbs, Boltzmann, and negative temperatures
- Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
- Heat and Fluctuations from Order to Chaos
- Smooth mixing Anosov flows in dimension three are exponential mixing
- On Thermostats: Isokinetic or Hamiltonian? finite or infinite?