Back Matter
# Glossary
Terms used technically throughout, with the chapter that introduces each.
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| --- | --- |
| Almost-periodic | A function whose $\delta$-near-recurrences form a relatively dense set. Equivalent, for a modular orbit, to having a purely atomic spectral measure. (Ch. 6) |
| Bures metric | The quantum Fisher information metric on state space; measures statistical distinguishability. (Ch. 10) |
| Cesàro mean | The running time-average $\frac1S\int_0^S$. Appears throughout because Wiener's theorem is a statement about it. (Ch. 6) |
| Coherence, $\mathcal{A}$ | The squared mass of the atoms of the modular spectral measure. Bounds the magnitude of valence. (Ch. 6) |
| Cosmopsychism | Panpsychism in which the whole is prior to the parts and subjects are quotients rather than sums. (Ch. 3) |
| Consonance, $\mathcal{C}$ | The $\kappa$-weighted spectral self-overlap; coherence refined by arithmetic simplicity of frequency ratios. (Ch. 7) |
| Einselection | Environment-induced superselection: decoherence picking out a preferred pointer basis. For a linearly coupled bosonic mode the pointer states are coherent states. (Ch. 5) |
| Factor | A von Neumann algebra with trivial centre — an indecomposable system. (Ch. 3) |
| Frustration, $\mathcal{D}$ | $\mathrm{Var}_P(q)$; the impossibility of satisfying all pairwise constraints at once. Sets the sign of valence. (Ch. 8) |
| Healing length, $\xi$ | The distance over which a Ginzburg–Landau order parameter recovers from a defect. Identified with the split collar $\varepsilon$. (Ch. 4) |
| Inverse participation ratio | $\sum_k\|c_k\|^4$; how concentrated a state is over a basis. Equals $\mathcal{A}$ for a discrete spectrum. (Ch. 6) |
| KMS condition | The analytic characterisation of thermal equilibrium. Every state is KMS with respect to its own modular flow. (Ch. 5) |
| Modular flow | The canonical one-parameter automorphism group $\sigma^\omega_s$ generated by an algebra and a state. Identified with phenomenal time. (Ch. 5) |
| Nuclearity | A bound on the density of states, satisfied by any theory with sensible thermodynamics; the technical hypothesis behind Theorem 3.1 and the split property. (Ch. 3) |
| Pure point / absolutely continuous | The atomic and density-carrying parts of a measure. Recurrence versus dispersal, by RAGE. (Ch. 6) |
| Replica symmetry breaking | Spontaneous breaking of the $\mathbb{Z}_n$ sheet-exchange symmetry of the replicated system; the signature of a rugged landscape. (Ch. 8) |
| Split property | The existence of a type I factor between strictly nested local algebras. The source of determinate subjects. (Ch. 4) |
| Superselection sector | A set of states that cannot be coherently superposed with states outside it. Makes phenomenal boundaries frame-invariant. (Ch. 4) |
| Thomae function | The "popcorn function", $1/q$ at each rational $p/q$ and $0$ at irrationals; the unsmoothed consonance kernel. (Ch. 7) |
| Type III$_1$ | The factor type of every local algebra in relativistic QFT: no minimal projections, no pure states, no trace. (Ch. 3) |
| Ultrametricity | $d(x,z)\le\max\{d(x,y),d(y,z)\}$; the hierarchical basin structure produced by RSB. (Ch. 8) |
| Uhlmann holonomy | The unitary acquired by parallel-transporting a state around a loop under the Bures connection. Proposed carrier of qualitative character. (Ch. 10) |
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