The factor counts unordered pairs once. For a symmetric interaction potential, this energy is unchanged by translating the entire probability measure. It therefore cannot have positive uniform displacement convexity on the unrestricted space containing translations. If , integrate the pointwise strong convexity inequality along an optimal transport plan and its independent copy. The variance identity for independent copies then gives -displacement convexity on every class with fixed barycenter of a measure, whenever the integrals are finite.
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Interaction energy refers to the energy associated with the interactions between two or more particles, atoms, or molecules. This concept is fundamental in various fields of physics and chemistry, as it helps describe how particles affect each other through forces. Interaction energy can manifest in different forms, depending on the type of interactions involved, such as: 1. **Gravitational Interaction Energy**: The potential energy due to the gravitational attraction between two masses.