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Equation 62 · Part 2 · The Entry a Relabeling Cannot Write

Symbol ρ

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

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 function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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