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Theorem

Virial Theorem

Mathematical Physics

For a stable, bound system of particles interacting through forces derived from a power-law potential, relates the long-term time-averaged total kinetic energy to the time-averaged potential energy by a fixed ratio depending on the power. First stated by Rudolf Clausius, it has applications from molecular physics to the dynamics of galaxy clusters.

Facts
Statement
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force, with that of the total potential energy of the system. 1
Proof Year
1870 1
Classification
Statement Form
Identity or Equation 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Sources
1. Virial Theorem (Wikipedia)
Wikimedia Foundation
  • Lead section, first sentence
    In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force, with that of the total potential energy of the system.
  • History section, first sentence
    In 1870, Rudolf Clausius delivered the lecture "On a Mechanical Theorem Applicable to Heat" to the Association for Natural and Medical Sciences of the Lower Rhine, following a 20-year study of thermodynamics.
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