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Equation 29 · Part 1 · The Entry a Relabeling Cannot Write

Symbol Δ E_Lambda

ΔEΛ(ρ)=0\Delta E_\Lambda(\rho) = 0
ΔEΛ\Delta E_\Lambda

What this part means

Δ ELE_Lambda is part of the quantity the equation computes from the expression on the right.

Its job in the formula

Δ ELE_Lambda is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…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: Δ\Delta EΛ(ρ)E_\Lambda(\rho) = 0 for every fine state ρ\rho if and only if DΛD_\Lambda = 0 as an operator identity, that is, if and only if Λ†(Hc)\Lambda^\dagger(H_c) = HfH_f exactly. Energy is preserved for every possible input under that one algebraic condition, never as a statistical tendency and never…

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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

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