Violation of detailed balance accelerates relaxation

TL;DR

This paper demonstrates that violating the detailed balance condition in Markov chain Monte Carlo methods universally accelerates convergence to equilibrium, revealing a thermodynamic inequality linking nonequilibrium and equilibrium relaxation processes.

Contribution

It provides a general proof that breaking detailed balance always speeds up relaxation, a finding not previously confirmed in broad contexts.

Findings

DBC violation always accelerates relaxation

Establishes a thermodynamic inequality relating nonequilibrium and equilibrium relaxation

Supports the potential for more efficient sampling algorithms

Abstract

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. Our result implies the existence of a kind of thermodynamic inequality that connects the nonequilibrium process relaxing toward steady state with the relaxation process which has the same probability distribution as its equilibrium state.