Equation 32 · Part 3 · The Entry a Relabeling Cannot Write

Symbol H_f

\Lambda^\dagger(H_c) = H_f

H_f

What this part means

$H_f$ is an input to the expression that computes the quantity on the left.

Its job in the formula

$H_f$ is an input to the expression that computes the quantity on the left.

Full expressionSymbol H_fArticle meaning

The passage around this formula

is a real number in units of energy for every fine state $\rho$ : how much the coarse description, evaluated through $H_c$ pulled back along $\Lambda$ , disagrees with the fine description’s own $H_f$ , for that specific state. Because expectation values determine a Hermitian operator uniquely — two Hermitian operators with the same trace against every density matrix are the same operator — the strongest statement follows at once: $\Delta$ $E_\Lambda(\rho)$ = 0 for every fine state $\rho$ if and…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

[9] Positive Functions on C*-Algebras ↗

These citations provide research context; check each source for the exact claim it supports.