Canonical ensemble describes a system where the number of particles ("N") and the volume ("V") is constant, and it has a well defined temperature ("T"), which specifies fluctuation of energy.

$\begingroup$ Thanks for your reply, but I fear you did not answer to some points.

Grand canonical ensemble Monte Carlo¶ In this example, a short grand canonical Monte Carlo simulation of Lennard Jones particles is conducted. Then, the ensemble becomes a collection of canonical ensemble with N, V, and T fixed. For fermions the wavefunction is antisymmetric. Bosons and Fermions in the Grand Canonical Ensemble Let us apply the Grand canonical formalism|see corresponding section of the Lecture Notes|to ideal Bose and Fermi gases. This lecture is a part of the statistical mechanics course for UG and PG syllabus of Indian Universities.

To construct the grand canonical ensemble, the system is enclosed in a container that is permeable both to heat and to the passage of particles.

The Grand Canonical Ensemble Last updated; Save as PDF Page ID 78454; Contributors; To consider theories for fluctuations in the number of particles we require an ensemble that keeps V, T, and the chemical potential, m constant, a grand canonical ensemble. In statistical mechanics, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. Holding its argument constant is consistent with your expression for $\left. Quantum Grand Canonical Ensemble How do we proceed quantum mechanically? Such density operator describes the maximum entropy ensemble distribution for a grand canonical ensemble--i.e., a collection of replica systems in thermal equilibrium with a heat reservoir whose temperature is as well as in equilibrium with respect to exchange of particles with a " particle" reservoir where the temperature is and the chemical potential of the particles is .

Abstract. The grand canonical ensemble is a statistical ensemble which is specified by the system volume V, temperature T, and chemical potential μ; the chemical potential is the energy which is necessary for adding one particle to the system adiabatically, and the detailed definition will be shown later. This statistical ensemble is highly appropriate for treating a physical system in which particles and energies …

$ The "correct" (conventional) Grand canonical ensemble expression contains a term that exactly cancels the "extra (nonsensical) term". An N particle basis function can be constructed in terms of single-particle wavefunctions as follows: ... of the grand partition function is

What you've explained is the usual role of the grand-canonical ensemble, a typical approach used also in … In this chapter, the grand canonical ensemble describing a system that exchanges energy and particles with the external world is introduced. There are two indices for summation since …