← All parts of this equation

Equation 65 · Part 2 · The Entry a Relabeling Cannot Write

Symbol rho_S

ρ=ρS⊗∣b⟩⟨b∣\rho = \rho_S \otimes |b\rangle\langle b|
ρS\rho_S

What this part means

rhoSo_S is an input to the expression that computes the quantity on the left.

Its job in the formula

rhoSo_S is an input to the expression that computes the quantity on the left.

The passage around this formula

Two limits inside this one formula answer different questions about how confidently the ledger can be interpreted. First, an uncorrelated, non-interacting bath: set HSBH_{SB} = 0 and let ρ\rho = ρS\rho_S ⊗\otimes |b⟩\rangle⟨\langle b| for any system state ρS\rho_S and any bath eigenstate |b⟩\rangle with HBH_B|b⟩\rangle = EbE_b|b⟩\rangle . Then Δ\Delta EΛ(ρ)E_\Lambda(\rho) = EbE_b for every choice of ρS\rho_S whatsoever — a pure constant, entirely independent of what the system is doing, unambiguously assignable…

Read this part in the article →

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 →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.