Manuscript Em03-F@1 · Em03-F-v1.tex · section · 0d4d148b

The switching apparatus supplies the work

Excess radiative energy and switching work › The switching apparatus supplies the work · lines 2234–2251

The source has $H_{S} = 0$ ; its internal energy cannot pay the positive energy in (eq:energy). Let $v_{R} = G_{R, D} f$ . The driven conditional reduced mean is

m_{s} = - s g v_{R} .

Define its classical Killing energy by

E_{cl} (t) = \frac{1}{2} \int [(\partial_{t} m_{s})^{2} + (\partial_{x} m_{s})^{2} + V m_{s}^{2}] d x .

It is finite because finite propagation gives compact Cauchy support at each finite time.

Displayed formulas in this passage

unlabeled · line 2240
$m_{s} = - s g v_{R} .$
unlabeled · line 2244
$E_{cl} (t) = \frac{1}{2} \int [(\partial_{t} m_{s})^{2} + (\partial_{x} m_{s})^{2} + V m_{s}^{2}] d x .$

Nearby in this section

proposition: Proposition: Exact switching-work ledger
section: The switching apparatus supplies the work