13 Facts About Statistical ensemble

In physics, specifically statistical mechanics, an ensemble is an idealization consisting of a large number of virtual copies of a system, considered all at once, each of which represents a possible state that the real system might be in.

In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a singlesystem.

Thermodynamic ensemble is a specific variety of statistical ensemble that, among other properties, is in statistical equilibrium, and is used to derive the properties of thermodynamic systems from the laws of classical or quantum mechanics.

For many important physical cases, it is possible to calculate averages directly over the whole of the thermodynamic Statistical ensemble, to obtain explicit formulas for many of the thermodynamic quantities of interest, often in terms of the appropriate partition function.

Precise mathematical expression for a statistical ensemble has a distinct form depending on the type of mechanics under consideration.

In classical mechanics, the Statistical ensemble is instead written as a probability distribution in phase space; the microstates are the result of partitioning phase space into equal-sized units, although the size of these units can be chosen somewhat arbitrarily.

The grand canonical Statistical ensemble is additionally a function of the particle number, measured by the total particle number operator.

In classical mechanics, an Statistical ensemble is represented by a probability density function defined over the system's phase space.

In statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the microstate of a system, according to the distribution of the system on its micro-states in this ensemble.

The grand canonical Statistical ensemble is an example of an open system.

Microcanonical Statistical ensemble represents an isolated system in which energy, volume and the number of particles are all constant.

The canonical Statistical ensemble represents a closed system which can exchange energy with its surroundings, but the volume and the number of particles are all constant.

The grand canonical Statistical ensemble represents an open system which can exchange energy as well as particles with its surroundings but the volume is kept constant.