= Oliver Penrose
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<Oliver Penrose>, with <Lars Onsager>, generalized <Bose-Einstein condensation> to interacting particles using the one-particle <reduced density matrix>. With its trace normalized to particle number $N$, condensation occurs when its largest eigenvalue grows proportionally to $N$, rather than remaining microscopic.<Bose-Einstein Condensation and Liquid Helium by Oliver Penrose and Lars Onsager>[Abstract and definition of condensation for interacting particles]{ref}
This defines macroscopic occupation without first assuming that an interacting liquid behaves like an ideal gas in a particular momentum state. The condensate fraction also need not equal the superfluid fraction: coherence and superfluid response are related physical questions, but not interchangeable numerical definitions.
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