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Ensemble average (statistical mechanics)

Index Ensemble average (statistical mechanics)

In statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the microstate of a system (the ensemble of possible states), according to the distribution of the system on its micro-states in this ensemble. [1]

20 relations: Canonical ensemble, Grand canonical ensemble, Hamiltonian mechanics, Information theory, Maxwell–Boltzmann statistics, Mean, Microcanonical ensemble, Microstate (statistical mechanics), Partition function (mathematics), Partition function (statistical mechanics), Phase space, Quantum mechanics, Quantum statistical mechanics, Stationary state, Statistical ensemble (mathematical physics), Statistical mechanics, Thermal equilibrium, Thermodynamic beta, Thermodynamic limit, Volume element.

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.

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Grand canonical ensemble

In statistical mechanics, a grand canonical 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.

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Hamiltonian mechanics

Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.

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Information theory

Information theory studies the quantification, storage, and communication of information.

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Maxwell–Boltzmann statistics

In statistical mechanics, Maxwell–Boltzmann statistics describes the average distribution of non-interacting material particles over various energy states in thermal equilibrium, and is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.

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Mean

In mathematics, mean has several different definitions depending on the context.

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Microcanonical ensemble

In statistical mechanics, a microcanonical ensemble is the statistical ensemble that is used to represent the possible states of a mechanical system which has an exactly specified total energy.

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Microstate (statistical mechanics)

In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations.

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Partition function (mathematics)

The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics.

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Partition function (statistical mechanics)

In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium.

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Phase space

In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Quantum statistical mechanics

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems.

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Stationary state

A stationary state is a quantum state with all observables independent of time.

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Statistical ensemble (mathematical physics)

In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1902, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in.

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Statistical mechanics

Statistical mechanics is one of the pillars of modern physics.

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Thermal equilibrium

Two physical systems are in thermal equilibrium if there are no net flow of thermal energy between them when they are connected by a path permeable to heat.

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Thermodynamic beta

In statistical mechanics, the thermodynamic beta (or occasionally perk) is the reciprocal of the thermodynamic temperature of a system.

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Thermodynamic limit

The thermodynamic limit, or macroscopic limit, of a system in statistical mechanics is the limit for a large number N of particles (e.g., atoms or molecules) where the volume is taken to grow in proportion with the number of particles.

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Volume element

In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates.

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References

[1] https://en.wikipedia.org/wiki/Ensemble_average_(statistical_mechanics)

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