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$H_{SB} \ne 0$

Why this formula appears here

Second, an entangled joint state with $H_{SB}$ $\ne$ 0 : now $\mathrm{Tr}$ [ $\rho$ $H_{SB}$ ] 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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H_{SB}

Symbol H_SB

$H_S$ B 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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Research cited beside this formula

[13] Quantum Thermodynamics ↗

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H_{SB} \ne 0

Equation 71 · 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 $H_{SB}$ $\ne$ 0 : now $\mathrm{Tr}$ [ $\rho$ $H_{SB}$ ] 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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HSB≠0H_{SB} \ne 0HSB​=0