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Equation 11 · Part 1 · The Entry a Relabeling Cannot Write

Symbol H_c

Hc=HS\mathcal H_c = \mathcal H_S
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 part of the quantity the equation computes from the expression on the right.

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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