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Equation 71 · Part 2 · The Entry a Relabeling Cannot Write

subscript

HSB≠0H_{SB} \ne 0
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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