Statistical theory can also be used in the microcanonical formalism to describe the excess energy partitioning in sequential dissociation steps, as proposed by Klots for a canonical ensemble.
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A variety of thermostat algorithms are available to add and remove energy from the boundaries of a MD simulation in a more or less realistic way, approximating the canonical ensemble.
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Another case in which the grand canonical ensemble appears is when considering a system that is large and thermodynamic ( a system that is " in equilibrium with itself " ).
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In this way, the canonical ensemble provides exactly the Boltzmann distribution ( also known as Maxwell Boltzmann statistics ) for systems of " any number " of particles.
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If the particles can be created out of energy during the dynamics of the system, then an associated term must not appear in the probability expression for the grand canonical ensemble.
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In general, it is desirable to apply the canonical ensemble to systems that are in direct contact with the heat bath, since it is that contact that ensures the equilibrium.
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The most general case is the probability distribution for the canonical ensemble, but also some special cases ( derivable from the canonical ensemble ) also show the Boltzmann distribution in different aspects:
48.
The most general case is the probability distribution for the canonical ensemble, but also some special cases ( derivable from the canonical ensemble ) also show the Boltzmann distribution in different aspects:
49.
In quantum mechanics, the grand canonical ensemble affords a simple description since diagonalization provides a set of distinct microstates of a system, each with well-defined energy and particle number.
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Another comment on redundancy, the article Maxwell-Boltzmann statistics contains 2 derivations ( second one is definitely correct, first one seems to be as well ) of the canonical ensemble.
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