Repulsive Influential Forces Induce Expansion of Information Radius

Mori, Tsutomu

doi:10.51094/jxiv.2166

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Mori, Tsutomu Department of Human Lifesciences, Fukushima Medical University School of Nursing https://researchmap.jp/read0186242

DOI:

https://doi.org/10.51094/jxiv.2166

キーワード:

information radius、 mutual information、 repulsive interactions、 information geometry、 natural forces

抄録

Mutual information (MI) and information radius provide complementary views on statistical dependence between interacting systems. Previous work has shown that attractive influential forces, aligned with the gradient of MI, induce a contraction of information radius under suitable regularity conditions. In this paper we develop the complementary theory of repulsive influential forces and prove that, under explicit regularity and sign assumptions on the force field, the information radius

r(t) = H(X_t) + H(Y_t) - 2 MI(X_t; Y_t)

evolves monotonically outward, in the sense that dr(t)/dt 竕･ 0 along any trajectory generated by such a repulsive influential force.

Within an information-theoretic dynamical framework, we decompose these forces into components that expand the marginals versus components that diminish MI, and express the resulting expansion rate in terms of variational identities for MI. This provides a rigorous expansion counterpart to contraction theorems for attractive influential forces and clarifies when informational repulsion can be realized by natural interactions. We discuss implications for phase separation, effective exclusion, and the organization of complex systems from an information-theoretic perspective.

利益相反に関する開示

The authors declare no potential conflict of interests.

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