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ΔEΛ(ρ)\Delta E_\Lambda(\rho)

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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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ΔEΛ\Delta E_\Lambda

Symbol Δ E_Lambda

Δ ELE_Lambda 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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ρ\rho

Symbol ρ

ρ 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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Published contexts (2)

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ΔEΛ(ρ)\Delta E_\Lambda(\rho)

Equation 73 · 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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ΔEΛ(ρ)\Delta E_\Lambda(\rho)

Equation 145 · Evolutionary Physics

The Entry a Relabeling Cannot Write

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

The honest limitation is not in any of those checks; it is in what the construction was never built to promise. Δ\Delta EΛ(ρ)E_\Lambda(\rho) is a number attached to one named channel and one named coarse Hamiltonian, not an observer-independent fact about “the” missing energy. A different, equally legitimate choice of Λ\Lambda — a different split of which few collective degrees of freedom count as “the system,” or a different unitary dilation of the same open dynamics, since Stinespring’s theorem guarantees a dilation exists but not that it is unique [ 9 ] — will generally return a different nonzero reading for the identical experiment, and nothing in the operator itself adjudicates which choice is…

Meanings in this article

  • ΔEΛ\Delta E_\Lambda: a number attached to one named channel and one named coarse Hamiltonian, not an observer-independent fact about “the” missing energy.
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