The Grand Canonical Ensemble: Theory and Applications
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##article.abstract##
The grand canonical ensemble (GCE) is an assembly structure with walls that the system or energy can penetrate. The ensemble is used in an open system that allows power and mass to exist with the environment. Only constant temperature and volume can limit the energy and number of systems in a GCE. As a result, the GCE differs in the number of systems and the amount of energy in each assembly. However, the total number of assemblies and the total amount of energy are constant. The purpose of this article is to explain the concept of the GCE and explain the implementation of the concept of the GCE in various fields. The application of the GCE concept in the physics study topics i.e. the equilibrium between the system and the particle energy reservoir, the grand partition function, the average number of occupations, semi-classical particles in integral formulations, the Bose-Einstein grand partition function, the Fermi-Einstein grand partition function, alternative formulation, and calculate the average number of particles. In addition to the application of the concept in the field of physics, there is also the implementation of the concept of a GCE in the field of chemistry, including determining the general equation of an ideal gas, a GCE approach to understanding the topic of electrochemical-thermodynamic studies, measuring fluctuations in the number of systems in the assembly and its relation to ion collisions, and the grand canonical Monte Carlo simulation. Each implementation has its use or purpose.
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