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Equation 73 · Part 3 · The Entry a Relabeling Cannot Write

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ΔEΛ(ρ)\Delta E_\Lambda(\rho)
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What this part means

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

The passage around this formula

Second, an entangled joint state with HSBH_{SB} ≠\ne 0 : now Tr\mathrm{Tr}[ρ\rho HSBH_{SB}] need not vanish, and, more importantly, it need not be assignable to “the system’s energy” or “the bath’s energy” separately at all. It is a property of the correlations in the joint state itself, a genuine interaction and correlation energy that a bipartite split has no vocabulary to divide further. Quantum thermodynamics has had to confront exactly this ambiguity in defining work, heat, and internal energy for open systems with non-negligible system-bath correlations, and the resolution adopted there is the one adopted here: report the total defect exactly, and do not pretend to resolve an assignment the…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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