system
Given the following post, respond as if you're commenting on Reddit:
human
Is it more energy efficient to leave the heater on low when nobody is home, or to heat it up from cold when you get back?

So this morning as I was the first to walk back into my freezing office after the holiday, I was reminded of an argument I used to have with my roommate when I lived in a drafty old house in upstate New York.  We would both leave the house for one to two weeks every Christmas, turning the thermostat down to something like 5C while we were away, and when we returned we would have to run the furnace full blast for about three days to get the house up to 22C again.  I would always suggest that it would be better leave the thermostat on something in the middle while were gone, like 15C, but he thought it was a waste of energy.  I argued that it took just as much energy to run the furnace continually for those three days when we returned than it did to maintain a modest temperature while we were away.  In reality, I have no idea, but I just hated those three days of feeling cold.

Obviously, this depends on lots of factors, like how cold it is outside and how long we are gone.  But in general, ignoring issues like pipes freezing, does it use more energy to maintain a moderate temperature for a long time and then heat it up for a short time, or to let something cool way down and then heat it up all the way?
gpt
The amount of heat lost by an object to the environment is proportional to the temperature difference between the environment and the object.

So if the object is at 20C, while the environment is at freezing (0C), then the rate of heat loss will be twice as high than if the object was at 10C.

If you keep heating the house while you're away, you keep the temperature higher and the total heat loss during your away time will be higher. Whereas if you turn the thermostat down very low, the rate of heat loss will gradually slow down as the house becomes colder and colder.

The total amount of energy you consume during this absence and the reheating that follows will be equal to the amount lost. In the case where you keep heating your house, this energy loss will be higher than in the case where you don't heat your house at every point in time (except for the initial period where the temperature drops from the starting point to your "something in the middle" value, in which case the energy loss is equal in both cases).

So from basic physics, it will be more efficient to turn the heater down as much as possible (without risk of freezing pipes) and heat it back up upon return. To overcome the discomfort of returning to a cold home, consider a smart thermostat that can be programmed to reach the desired temperature when you return (and will start to heat before you get back). Some can even "learn" how long it takes to heat up your house specifically with repeated use, so that they start at the exact right time.