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Equation 8 · Part 1 · The Entry a Relabeling Cannot Write

Symbol H_c

Hc\mathcal H_c
HcH_c

What this part means

wrong, does not touch the total energy of any closed system, and does not by itself explain where a nonzero reading comes from.

Its job in the formula

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

Where the article explains it

It does not propose that HfH_f or HcH_c is wrong, does not touch the total energy of any closed system, and does not by itself explain where a nonzero reading comes from; it only names, precisely and checkably, how large the disagreement is between two fully specified descriptions.

The passage around this formula

A coarse description reports less. It is built from a completely positive, trace-preserving map Λ\Lambda , a quantum channel sending fine states to coarse states, together with a coarse Hilbert space Hc\mathcal H_c and a Hermitian coarse Hamiltonian HcH_c on it. The simplest case is the partial trace over the bath, Λ(ρ)\Lambda(\rho) = TrB\mathrm{Tr}_B[ρ\rho] with Hc\mathcal H_c = HS\mathcal H_S ; nothing below depends on that particular choice, and a passive relabeling built from no discarding at all, treated next, is a channel too.

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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.

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Sources cited in the article section

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