[mshanowitz]

Just want to point out that this argument is not universally accepted by modern halachic (Jewish law) authorities.

Shlomo Zalman Auerbach, a very prominent orthodox Jewish halachist held that closing/opening an electrical circuit does not constitute the biblical prohibition of building and destroying.

Instead, he held that that electricity was prohibited "Rabbinically" for an unrelated reason (which is of a lower degree of severity, which has practical implications).

Notwithstanding this, if one say, turns on an incondescent lightbulb I believe that is biblically prohibited according to all because of the heat it generates.

[lebuffon]

Can you make a switch Kosher by putting 1M ohm resistor across it. Then the circuit would never be broken just modified. Electric Eruvin? (Consult your local Rabbi) I think that was done to touch-tone telephones in Israel many years ago when we still used land lines.

[reissbaker]

"Sabbath mode" ovens work in a clever way, where the temperature switch is only checked on a certain interval. So when you change the temperature you're generally not completing or breaking a circuit, since the circuit is likely currently broken anyway.

Most rabbinic authorities still prohibit Sabbath mode ovens on Shabbat for different reasons, but on holidays with weaker restrictions but that still have electricity bans, like Passover, permit their use.

I remember when my parents first got a "Sabbath mode" oven, the local Orthodox rabbi came over excitedly just to see it at work.

[mshanowitz]

There is an organization in Israel, Tzomet, dedicated to these kind of stuff. I believe they manufacture such products.

But they're explicitly dedicated for times of need and not for leisure purposes.