Equation 62 · The Entry a Relabeling Cannot Write
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol Δ E_Lambda
Δ ambda is part of the quantity the equation computes from the expression on the right.
Symbol ρ
ρ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol I_S
is one of the signed contributions combined to compute the quantity on the left.
Symbol H_B
is one of the signed contributions combined to compute the quantity on the left.
Symbol H_SB
B is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →change
Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.
subscript
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.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
an exact operator identity, not an approximation valid in some limit: the ledger for a system-only description of a system-plus-bath is precisely the bath’s own energy plus the coupling energy between the two, nothing more and nothing less. = [] for any joint state .
Sources cited in the article section
These citations give research context. Read each source to check which claims it supports.
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