Symbol H_c
is part of the quantity the equation computes from the expression on the right.
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Why this formula appears here
Passive relabeling is one degenerate case; the other is simpler still. Let be the identity channel, = , = : no relabeling, no discarding, the coarse description simply is the fine one. Then trivially = 0 . Nothing in the paragraphs above required that; it follows on inspection. But the triviality is the point, because this is the operator-language shadow of the oldest and most secure fact the subject has. A system evolving under its own Hamiltonian, with nothing coarse-grained away and nothing relabeled, conserves that Hamiltonian’s own expectation value exactly, because the Hamiltonian generates its own time evolution and commutes with…
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Symbol H_f
is an input to the expression that computes the quantity on the left.
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Read it with the definitions, units, and assumptions supplied by the article.
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Published contexts (2)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 52 · Evolutionary Physics
The Entry a Relabeling Cannot Write
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Passive relabeling is one degenerate case; the other is simpler still. Let be the identity channel, = , = : no relabeling, no discarding, the coarse description simply is the fine one. Then trivially = 0 . Nothing in the paragraphs above required that; it follows on inspection. But the triviality is the point, because this is the operator-language shadow of the oldest and most secure fact the subject has. A system evolving under its own Hamiltonian, with nothing coarse-grained away and nothing relabeled, conserves that Hamiltonian’s own expectation value exactly, because the Hamiltonian generates its own time evolution and commutes with…
Equation guide → · Article →Equation 134 · Evolutionary Physics
The Entry a Relabeling Cannot Write
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
the detuned Hamiltonian that governs spin precession in a frame rotating with an applied field — the identical construction I. I. Rabi used to analyze spin behavior in a gyrating magnetic field in 1937 [ 14 ] . Two checks confirm the recovery is exact rather than incidental: at = 0 , the non-rotating case, 0 and = , the already-verified baseline; at = , exact corotation, = 0 and the spin’s energy in this frame vanishes identically, which is the ordinary resonance condition, not a puzzle, because = -/2 exactly cancels the lab-frame value for a state that starts, and stays,…
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