Does true thermal equilibrium take an infinite amount of time to reach? That is to say, is thermal equilibrium reached asymptotically? I intuitively visualize thermal equilibrium as the gradual homogenization of temperature, but I can't see how it would actually reach it in a finite amount of time.
 A: In practice, there almost always is a "background noise" temperature that furnishes a floor for measurement sensitivity. Once the temperature or temperature difference you are looking for falls below that floor, the signal is gone even if it has not yet asymptotically gone all the way to zero.
A: This is a very good question.
Indeed, temperature homogenization takes place as long as there is a driving force on the temperature.
But the driving force implies a temperature difference.
So the very definition of heat forces the Zero Principle to be reached in infinite time.
However, in real life there are always irreversibilities, which occur covertly.
Thus a room would inevitably dissipate heat by radiation through the outer walls, altering the temperature equalization of the system.
This breaks the riddle.
There was a Greek tale called Achilles and the Tortoise that was put together in the pre-Socratic era.
Here is a video about it
https://www.youtube.com/watch?v=skM37PcZmWE
I've given it a lot of thought myself.
