How is negative temperature hotter than infinite temperature?

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edit: refer to [this link](https://en.wikipedia.org/wiki/Negative_temperature) for further explanation

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You’ll need to supply some context, because in conventional physics with real numbers what you are asking is about two impossible states.

Negative temperature would require something less than absolute zero, which is where all thermal energy, which could be described as the average of movement values, stops. Since a negative vector still has a value, this is like asking for the square root of a negative number: it requires something outside of ‘real’ numbers.

Infinite is impossible to reach with real numbers by definition; every real number can be added to, while infinite can’t.

If you are asking about a specific theoretical physics statement, post a link so others can take a look at it.

Do you have any further explanation on what is negative and infinite temperature?

In conventional physics, neither negative nor infinite temperatures are a thing. Think of temperature as a measure of how fast the molecules of a thing are moving around. The faster the molecules, the hotter thin thing. When there is no movement at all, that is Absolute Zero, the lowest possible temperature at 0K, or -273.15°C. You can’t move slower than stopped. There is also a limit to how fast things can move, the speed of light. When the molecules in a thing are going at the speed of light, the thing reaches “absolute hot”, or the Plank Temperature, of 1.42 x 10^(32) °C Nothing in the known universe is even close to reaching that.

In Statistical mechanics, temperature is defined by how much entropy you get from adding some energy to the system (Specifically, 1/T=ds/dE). In the most common case of particles in a 3D universe, adding energy always increases entropy, so temperature is always positive.

It is possible to construct a scenario where adding energy to a system causes the entropy to decrease, which would make the temperature negative. In these scenarios, it generally only happens at energy levels above the states with positive temperature

Basically, it requires using a definition of temperature that isn’t particularly relevant in day-to-day life, and a scenario that takes advantage of that particular definition.

Temperature isn’t defined how you think, it’s about a relationship between energy and entropy not just about energy. Irrelevant for daily life but results in negative temperature quirks being possible

Positive temperature means that as you add energy to a system entropy increases, electrons pick up more energy and are spread across more energy levels

Negative temperature means you add energy and entropy decreases

This is generally not possible unless you’ve done something to constrain what states electrons can hop into like with lasers in a lab. With the now limited number of states you can pump energy into the atoms until none of the electrons are in low energy levels so every bit of new energy concentrates them in the higher energy state which reduces entropy as there’s less variation

Energy will always flow from “hot” to “cold” unless acted upon like with a heat pump. Energy will always flow from something with Negative temperature to something with positive temperature until the negative temperature state is eliminated.