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Mutual Energy


Let Omega be a space with measure mu>=0, and let Phi(P,Q) be a real function on the product space Omega×Omega. When

(mu,nu)=intintPhi(P,Q)dmu(Q)dnu(P)
(1)
=intPhi(P,mu)dnu(P)
(2)

exists for measures mu,nu>=0, (mu,nu) is called the mutual energy. (mu,mu) is then called the energy.


See also

Energy

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References

Iyanaga, S. and Kawada, Y. (Eds.). "General Potential." §335.B in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1038, 1980.

Referenced on Wolfram|Alpha

Mutual Energy

Cite this as:

Weisstein, Eric W. "Mutual Energy." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MutualEnergy.html

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