Manuscript En07-C@1 · En07-C.tex · definition · 3f7e9ebb

Definition: A specified conserving energy ledger

Entropy, energy, erasure cost, and leakage › The complete energy ledger · lines 1319–1334

En07-C@1#def:energy, En07-C@1#eq:unitary-energy, En07-C@1#eq:isometric-energy

For a complete unitary $U$ on a finite system with declared Hamiltonian $H_{tot}$ , exact conservation means

U^{†} H_{tot} U = H_{tot} .

For an isometry between declared input and output energy spaces, the stronger intertwining form is

H_{out} V = V H_{in} .

These are additional hypotheses.

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