Thanks for the simple answer. Wouldn’t temperature still be intrinsic? Assuming there’s only one particle in the universe it would still have a temperature right? Yes it’s not in relation to anything but then neither would charge be in our one particle example. I am the merest amateur so bear with me.
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No, it would only have a state. In classical physics the state would be its Kinetic energy. In QE it would be.... well it’s state.
T is only defined in an ensemble of other particles, i.e. when you can no longer keep track the particles and it’s necessary to use averages. Then the T is the average kinetic energy.
Furthermore T is only technically defined in thermodynamic equilibrium, so nothing happens at all (otherwise you’re not in equilibrium).
Finally, you can have “negative temperature” I.e T < absolute zero, if you have population inversion (I.e. a lasing cavity) which is really an abuse of nomenclature since population inversion cannot occur in equilibrium (and therefore T is not defined). However, the Boltzmann (?) equations have pop inv. only when the the T parameter is negative (even though pop inv. is the “hotter” than infinitely hot).
All this to say that 1. T is not defined for a single particle 2. T is not well defined for very many systems at all!
Assuming there’s only one particle in the universe it would still have a temperature right?
Not really.
One (not quite universal) way to think of temperature is as a measure of average energy per degree of freedom (linear motion, rotational motion, vibration, ...). This assumes a system where random interactions spread the energy throughout, exciting all these different energy states. In contrast, when you take your single particle and add some energy, there's no spreading of anything and no excitation of other degrees of freedom - the system doesn't 'thermalize', and no average emerges.
Note that there are other ways to think about this, eg in terms of inverse temperature (thermodynamic beta), which is essentially a measure of phase space growth under addition of energy. Your single particle system will only exist in a single state no matter how much energy you add, so it's not really useful to take a thermodynamic approach...
When you say "the gas in this container is 100'C," that is a statement about the vibration and motion of the molecules which constitute that gas. To say something is hot or cold is to say that the average molecule in that substance has or lacks kinetic energy. Therefore, temperature is a description of the kinetic motion in a system, and so it emerges from position and velocity.
Source: also an amateur
An easier example to think about might be pressure. A single molecule free in a vacuum can’t be said to have a pressure, but put it in a container along with a few other molecules and it starts to become a useful property to measure and think about.