A multivariate generalization of mutual information, multi-information, is defined in the thermodynamic limit. The definition takes phase coexistence into account by taking the infimum over the translation-invariant Gibbs measures of an interaction potential. It is shown that this infimum is attained in a pure state. An explicit formula can be found for the Ising square lattice, where the quantity is proved to be maximized at the phase-transition point. By this, phase coexis-tence is linked to high model complexity in a rigorous way.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:32604 |
| Date | 07 January 2019 |
| Creators | Erb, Ionas, Ay, Nihat |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 0022-4715, 1572-9613 |
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