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The canonical ensemble is the ensemble that describes the possible states of a system that is in thermal equilibrium with a heat bath (the derivation of this fact can be found in Gibbs [1]). The canonical ensemble applies to systems of any size; while it is necessary to assume that the heat bath is very large (i.e., take a macroscopic limit ...
The grand canonical ensemble is the ensemble that describes the possible states of an isolated system that is in thermal and chemical equilibrium with a reservoir (the derivation proceeds along lines analogous to the heat bath derivation of the normal canonical ensemble, and can be found in Reif [3]).
Each of these is assumed to be constant in the ensemble. For this reason, the microcanonical ensemble is sometimes called the NVE ensemble. In simple terms, the microcanonical ensemble is defined by assigning an equal probability to every microstate whose energy falls within a range centered at E. All other microstates are given a probability ...
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Although the heat bath of Nosé–Hoover thermostat consists of only one imaginary particle, simulation systems achieve realistic constant-temperature condition (canonical ensemble). Therefore, the Nosé–Hoover thermostat has been commonly used as one of the most accurate and efficient methods for constant-temperature molecular dynamics ...