1999
DOI: 10.1063/1.477973
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Strict detailed balance is unnecessary in Monte Carlo simulation

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.

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Cited by 161 publications
(159 citation statements)
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“…Under the condition that the Hamiltonian evolution is ergodic in the microcanonical ensemble, it follows that our method samples the canonical ensemble. 12 More precisely, Hamilton's equations sample a phase-space surface with fixed center of mass and, for non-periodic systems, zero angular momentum. Since the rescaling procedure does not change these quantities, our algorithm samples only the corresponding slice of the canonical ensemble.…”
Section: Theory a A Canonical Velocity-rescaling Thermostatmentioning
confidence: 99%
“…Under the condition that the Hamiltonian evolution is ergodic in the microcanonical ensemble, it follows that our method samples the canonical ensemble. 12 More precisely, Hamilton's equations sample a phase-space surface with fixed center of mass and, for non-periodic systems, zero angular momentum. Since the rescaling procedure does not change these quantities, our algorithm samples only the corresponding slice of the canonical ensemble.…”
Section: Theory a A Canonical Velocity-rescaling Thermostatmentioning
confidence: 99%
“…It should be noted that although the detailed balance conditions is sufficient, it is not a necessary condition as shown e.g. in [31].…”
Section: Monte Carlo and The Metropolis Algorithmmentioning
confidence: 99%
“…Thermal-equilibrium sampling by Markov methods New Markov-chain methods for thermal-equilibrium sampling are usually justified using the principle of detailed balance, but here we prefer to base our arguments on the more general principle of "balance." 27 We start by recalling briefly what this principle is. For simplicity, we shall refer in this section to systems having discrete sets of states .…”
Section: Basic Principlesmentioning
confidence: 99%