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Equation 57 · Part 2 · The Entry a Relabeling Cannot Write

Symbol ρ

Λ(ρ)=TrB[ρ]\Lambda(\rho) = \mathrm{Tr}_B[\rho]
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

Return to the genuine coarse-graining set aside earlier: Λ(ρ)\Lambda(\rho) = TrB\mathrm{Tr}_B[ρ\rho] , Hc\mathcal H_c = HS\mathcal H_S , HcH_c = HSH_S . The dual embeds a system observable back into the full space without touching the bath, Λ†(HS)\Lambda^\dagger(H_S) = HSH_S ⊗\otimes IBI_B , so

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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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