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Tr[ρHSB]\mathrm{Tr}[\rho H_{SB}]

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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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ρ\rho

Symbol ρ

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HSBH_{SB}

Symbol H_SB

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

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Tr[ρHSB]\mathrm{Tr}[\rho H_{SB}]

Equation 72 · Evolutionary Physics

The Entry a Relabeling Cannot Write

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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