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====== Entropy of pure states: not all wave functions are born equal ====== **Denis Sunko**\\ Department of Physics\\ Faculty of Science, University of Zagreb\\ Zagreb, Croatia\\ <blockquote> Many-fermion Hilbert space is a finitely generated free module. The generators of the module, called shapes, are precisely all N-fermion primitive realizations of the Pauli principle. They are geometric objects in wave-function space, which constrain fermion motion kinematically. Although the number of shapes is absolutely very large, N!d-1 for N fermions in d dimensions, it is finite and vanishingly small relative to the total number of excited states in the same energy range. The majority of states, called trivial, can be constructed as bosonic excitations of the shapes. This algebraic structure is analysed from the point of view of entropy. The shapes naturally form a lattice partially ordered by information content, even though they are all pure states with zero von Neumann entropy. </blockquote>