Virial theorem

The virial theorem is a feature of systems with central forces.

{\overline {\mathcal {V}}}=-{\frac {1}{2}}{\overline {\sum _{i}{\frac {dU}{dr}}\cdot r_{i}}}

The overlines represent time averages. The right hand side is known as the virial of Clausius ^[1]. (Note: Herbert Goldstein uses $T$ for the virial ^[2], however here we use T for temperature, thus we use ${\mathcal {V}}$ as per Hansen and McDonald^[3]).

References

↑ R. Clausius, "XVI. On a mechanical theorem applicable to heat" Philosophical Magazine 40 pp. 122-127 (1870)
↑ Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002) § 3.4
↑ Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition) Eq. 2.2.5

Related reading

J. C. Slater "The Virial and Molecular Structure", Journal of Chemical Physics 1 pp. 687-691 (1933)

[1] R. Clausius, "XVI. On a mechanical theorem applicable to heat" Philosophical Magazine 40 pp. 122-127 (1870)

[2] Herbert Goldstein, Charles P. Poole, Jr. and John L. Safko "Classical Mechanics" (3rd edition) Addison-Wesley (2002) § 3.4

[3] Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition) Eq. 2.2.5

[1]

[2]

[3]

Virial theorem

References

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