| Summary: | The grand canonical ensemble refers to thermodynamic states that are determined through the temperature, the volume and the chemical potential, that is to open systems at equilibrium. Through the general method first the probability of microstates is obtained and then the mean values and fluctuations of the macroscopic variables. The ensemble is applied to simple systems and then to cases where the number of particles fluctuate, as in chemical systems at equilibrium and quantum systems. In the latter case the Fermionic and Bosonic character of quantum systems is employed for the determination of their statistical and physical properties. In the limit of high temperature, both cases converge to the classical ensemble limit.
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