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Equation 62 · Part 1 · The Entry a Relabeling Cannot Write

Symbol Δ E_Lambda

ΔEΛ(ρ)=Tr[ρ(IS⊗HB+HSB)]\Delta E_\Lambda(\rho) = \mathrm{Tr}[\rho(I_S \otimes H_B + H_{SB})]
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

an exact operator identity, not an approximation valid in some limit: the ledger for a system-only description of a system-plus-bath is precisely the bath’s own energy plus the coupling energy between the two, nothing more and nothing less. Δ\Delta EΛ(ρ)E_\Lambda(\rho) = Tr\mathrm{Tr}[ρ(IS⊗HB+HSB)\rho(I_S \otimes H_B + H_{SB})] for any joint state ρ\rho .

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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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