Strict Detailed Balance is Unnecessary in Monte Carlo Simulation

TL;DR

This paper demonstrates that Monte Carlo simulations do not require strict detailed balance, but only a weaker balance condition, broadening the scope of valid algorithms and confirming the correctness of new methods that preserve the Boltzmann distribution.

Contribution

It proves that weaker balance conditions suffice for Monte Carlo validity, enabling new algorithms beyond traditional detailed balance constraints.

Findings

Sequential updating schemes are valid under weaker balance conditions.

A new class of methods that leave the Boltzmann distribution invariant is correct.

Strict detailed balance is not necessary for Monte Carlo simulation validity.

Abstract

Detailed balance is an overly strict condition to ensure a valid Monte Carlo simulation. We show that, under fairly general assumptions, a Monte Carlo simulation need satisfy only the weaker balance condition. Not only does our proof show that sequential updating schemes are correct, but also it establishes the correctness of a whole class of new methods that simply leave the Boltzmann distribution invariant.