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Equation 73 · Part 2 · The Entry a Relabeling Cannot Write

Symbol ρ

ΔEΛ(ρ)\Delta E_\Lambda(\rho)
ρ\rho

What this part means

ρ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

ρ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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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