These simulations typically utilize algorithms based upon molecular dynamics or microcanonical ensemble algorithms.
2.
The preferred solution to these problems is avoid use of the microcanonical ensemble.
3.
In practice, the microcanonical ensemble does not correspond to an experimentally realistic situation.
4.
In statistical mechanics, the microcanonical ensemble is a particular microstates with equal probability.
5.
This feature is an unavoidable consequence of requiring that the microcanonical ensemble is a steady-state ensemble.
6.
The Monte Carlo simulation of a microcanonical ensemble thus requires sampling different microscopic states with the same energy.
7.
Moreover there are ambiguities regarding the appropriate definitions of quantities such as entropy and temperature in the microcanonical ensemble.
8.
The microcanonical ensemble is a collection of microscopic states which have fixed energy, volume and number of particles.
9.
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.
10.
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.
