Statistical Mechanics - Canonical Ensemble : Energy Fluctuations in Canonical Ensemble
In the canonical ensemble, the energy E of the system is not fixed, but varies. On the other hand, the energy of a system in the microcanonical ensemble is almost fixed to a given value. But the thermodynamic properties of a system derived through these two approaches are identical. Thus, these two approaches are consistent. It is found that the relative rms fluctuation in E is inversely proportional to the square root of the number of particles in the system. As number of the particles in statistical system is very large so the relative rms fluctuation in E is negligible and energy almost remain constant, like a Micro canonical ensemble and so both ensembles are identical and they will practically yield the identical results.
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