What do you mean by canonical and grand canonical ensemble?

In statistical mechanics, a grand canonical ensemble (also known as the macrocanonical ensemble) is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that are in thermodynamic equilibrium (thermal and chemical) with a reservoir.

What do you understand grand canonical?

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.

What is stationary ensemble?

The concept of an equilibrium or stationary ensemble is crucial to many applications of statistical ensembles. Such a statistical ensemble, one that does not change over time, is called stationary and can be said to be in statistical equilibrium.

What is the difference between a canonical ensemble and a microcanonical ensemble?

Microcanonical ensemble means an isolated system with defined energy. The system may be found only in microscopic state with the adequate energy, with equal probability. Canonical ensemble means a system attached to the “temperature reservoir”, which may supply/take infinite amount of energy.

What is the difference between microcanonical and canonical ensemble?

Why do we need different ensembles in statistical mechanics?

It is not necessary to define any other ensemble, but it is convenient. If your system for instance is in contact with a big other system (“reservoir”) with which it can exchange energy, then you can either describe system plus reservoir microcanonically, or you describe only your system canonically.

What is the partition function for microcanonical ensemble?

An important point about the canonical ensemble is that we derived a result about the system only. The partition function is a sum over microstates of the system. Pk is the probability of nding the system in microstate k when it is in equilibrium at a temperature T no matter what it is in contact with.

What do you mean by ensemble and 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. The system can exchange energy with the heat bath, so that the states of the system will differ in total energy.

What is grand partition function?

Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential.

Microcanonical ensemble means an isolated system with defined energy. The system may be found only in microscopic state with the adequate energy, with equal probability. Canonical ensemble means a system attached to the “temperature reservoir”, which may supply/take infinite amount of energy.

How does grand canonical ensemble relate to experiment?

Grand canonical ensemble describes a system with fixed volume (“V”) and temperature (“T”) but to specify the fluctuation of the number of particles it introduces chemical potential (“mu”). But, how does that relate to experiment? Can you give me real life examples for those ensembles.

How to create a canonical NVT ensemble?

Typically (at least how I learned this after three years of chemistry) the canonical NVT ensemble is created by considering many microcanonical NVE “ensembles” as microstates in this NVT ensemble. I quote from my lecture script for statistical thermodynamics: