These simulations typically utilize algorithms based upon molecular dynamics or microcanonical ensemble algorithms.
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The preferred solution to these problems is avoid use of the microcanonical ensemble.
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In practice, the microcanonical ensemble does not correspond to an experimentally realistic situation.
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In statistical mechanics, the microcanonical ensemble is a particular microstates with equal probability.
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This feature is an unavoidable consequence of requiring that the microcanonical ensemble is a steady-state ensemble.
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The Monte Carlo simulation of a microcanonical ensemble thus requires sampling different microscopic states with the same energy.
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Moreover there are ambiguities regarding the appropriate definitions of quantities such as entropy and temperature in the microcanonical ensemble.
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The microcanonical ensemble is a collection of microscopic states which have fixed energy, volume and number of particles.
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Gibbs investigated carefully the analogies between the microcanonical ensemble and thermodynamics, especially how they break down in the case of systems of few degrees of freedom.
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The condition that the ETH imposes on the diagonal elements of an observable is responsible for the equality of the predictions of the diagonal and microcanonical ensembles.
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