In thermodynamics, an ensemble is a collection of many copies of a physical system that can be studied statistically. Two commonly used ensembles in statistical thermodynamics are the microcanonical ensemble and the grand canonical ensemble.
The microcanonical ensemble refers to a fixed NVE (number of particles, volume, and total energy) system. In this ensemble, the system is assumed to be isolated, meaning that it exchanges neither matter nor energy with its surroundings. The energy of the system is fixed, and the system is assumed to be in equilibrium. In this ensemble, every possible configuration of the system with a given total energy is equally likely.
On the other hand, the grand canonical ensemble refers to a system that is not isolated but is in contact with a heat bath and a particle reservoir. This ensemble considers a system that is open, meaning that it can exchange particles, energy, and volume with its surroundings. In this ensemble, the temperature, volume, and chemical potential of the system are not fixed. Instead, the average number of particles in the system is determined by the chemical potential of the particle reservoir.
In summary, the difference between the microcanonical and grand canonical ensembles lies in the constraints imposed on the system. The microcanonical ensemble describes a fixed NVE system, whereas the grand canonical ensemble describes a system that can exchange particles, energy, and volume with its surroundings.