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Statistical ensemble

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Summary

A probability measure over classical microstates or a density operator over a quantum state space, chosen to represent preparation constraints and calculate expectation values.

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Incoming relations (arrows to this concept)

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Probability distributionStatistical ensemble

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

A classical statistical ensemble is formulated as a probability measure on a specified microstate space. Quantum ensembles instead use density operators, so the probability-distribution formulation is not the whole target concept.

How to interpret this relation type

A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.

Relation sources

Statistical mechanicsStatistical ensemble

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

An ensemble is the probabilistic state description used to average observables over classical or quantum microscopic alternatives.

How to interpret this relation type

The target represents a state, property, observable, or state-dependent description associated with the source system or theory.

Relation sources

Outgoing relations (arrows from this concept)

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Statistical ensembleCanonical ensemble

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

The canonical ensemble is the equilibrium ensemble for energy exchange with a temperature reservoir at fixed remaining controls.

How to interpret this relation type

The target is a member or subtype of the broader source class.

Relation sources

Statistical ensembleGibbs entropy

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Gibbs entropy is a functional of the ensemble probabilities or density operator, with the reference measure and quantum trace specified.

How to interpret this relation type

The target represents a state, property, observable, or state-dependent description associated with the source system or theory.

Relation sources

Statistical ensembleGrand-canonical ensemble

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

The grand-canonical ensemble permits energy and particle exchange and weights states using temperature and chemical potential.

How to interpret this relation type

The target is a member or subtype of the broader source class.

Relation sources

Statistical ensembleMicrocanonical ensemble

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

The microcanonical ensemble is the equilibrium ensemble selected by isolation and fixed conserved quantities, including an energy shell.

How to interpret this relation type

The target is a member or subtype of the broader source class.

Relation sources