Sampling and statistical physics via symmetry

TL;DR

This paper introduces a symmetry-based framework for Markov chain Monte Carlo sampling and statistical physics, leading to new algorithms and insights into effective temperature and energy from data.

Contribution

It presents a novel symmetry perspective that derives existing MCMC algorithms, proposes a faster parallel algorithm, and offers a practical method to analyze physical systems from data.

Findings

New parallel MCMC algorithm with faster convergence

Framework for defining effective temperature and energy from data

Application to Anosov systems demonstrating practical utility

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.