To the extent that you want to define something that allows you to characterize a boiling pot of water as having either zero entropy or zero temperature, define away.
It's not an arbitrary definition made for fun. It is - as I've pointed out - the only definition that is consistent. Any other set of definitions will lead to 'paradoxes', like Maxwell's demon or various other 'violations' of the 2nd law.
I will point out that your quantities of "entropy" and "temperature" break the laws of thermodynamics in probably every respect.
On the contrary, they are the only consistent way of looking at thermodynamics.
In your system, energy can flow from a colder object to a hotter object.
And why not? Every time a battery powers an (incandescent) flashlight, energy is flowing from a colder object to a hotter object.
It seems to me the only point is to piggyback your relatively useless concepts on the well-deserved reputation of entropy and temperature in order to get them an attention they do not deserve.
The point is to put thermodynamics on a rigorous and general footing. That's why Jaynes and others proposed MaxEnt thermodynamics.
No matter how much information I have about a pot of boiling water, it is still capable of turning a turbine with its steam, cooking rice, and melting ice cubes
These things you speak of are due to the energy in the boiling water, not the temperature, and energy is not changed no matter how much you know about the system. A system at 0 K can still carry energy. There is nothing in the laws of physics that prevents this.
And why not? Every time a battery powers an (incandescent) flashlight, energy is flowing from a colder object to a hotter object.
Actually, no. The temperature of the electrons moving in the current is quite high. At least according to the uncontroversial definitions generally used. These electrons have a lot of kinetic energy.
A system at 0 K can still carry energy. There is nothing in the laws of physics that prevents this.
Actually there is. 0 K is the state where no further energy can be extracted from the system. So a 0 K system can't do wo...
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