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Equation 69 · Part 2 · The Entry a Relabeling Cannot Write

Symbol ρ

ΔEΛ(ρ)=Eb\Delta E_\Lambda(\rho) = E_b
ρ\rho

What this part means

ρ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

ρ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

Two limits inside this one formula answer different questions about how confidently the ledger can be interpreted. First, an uncorrelated, non-interacting bath: set HSBH_{SB} = 0 and let ρ\rho = ρS\rho_S ⊗\otimes |b⟩\rangle⟨\langle b| for any system state ρS\rho_S and any bath eigenstate |b⟩\rangle with HBH_B|b⟩\rangle = EbE_b|b⟩\rangle . Then Δ\Delta EΛ(ρ)E_\Lambda(\rho) = EbE_b for every choice of ρS\rho_S whatsoever — a pure constant, entirely independent of what the system is doing, unambiguously…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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