Manuscript Hawk02-E@1 · Hawk02-E.tex · section · 4841592b

Energy ledger

Complete channels and exact microscopic accounting › Energy ledger · lines 840–853

For a prescribed differentiable switching schedule $g_{a} (t)$ , a separate time-dependent model has the work term

\frac{d}{d t} ⟨ H (t)⟩ = a \sum g ˙_{a} (t) ⟨ A_{a} \otimes Φ (f_{a})⟩ .

A switch used in a gravitational comparison must retain this work. It is not an autonomous endpoint operation.

Displayed formulas in this passage

unlabeled · line 844
$\frac{d}{d t} ⟨ H (t)⟩ = a \sum g ˙_{a} (t) ⟨ A_{a} \otimes Φ (f_{a})⟩ .$