Toy Josephson Coupling

Coupling Sign Changes the Energy Direction

A signed flux source flips the direction of the toy coupling energy ledger while the current magnitude stays fixed. The sign change is exact only for the declared sign convention and input values; real circuits must account for bias calibration, phase offsets, noise, and readout interpretation.

A signed flux source fixes the sign of the toy coupling. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Changing flux sign changes the energy sign

The current stays 3 amperes, but the flux is -2 webers.

3 A⋅−2 Wb=−6 J3\ \text{A}\cdot -2\ \text{Wb}=-6\ \text{J}
Signed couplingThe sign is derived from signed flux.current=3 Aflux=-2 WbcouplingFactor=1couplingEnergy=-6 J

A label cannot choose the sign

The checked toy energy is -6 joules because the flux source is negative.

Etoy=−6 JE_{\text{toy}}=-6\ \text{J}
Signed sourceA stale positive energy would fail validation.current=3 Aflux=-2 WbcouplingFactor=1couplingEnergy=-6 J