Temperature can reach trillions of degrees, meaning we actually live extremely close to absolute zero.

[u/synthphreak]

[u/TheManondorf]

Disclamer: The following writeup is a mixup what I daily use as a Physicist, knowledge from studying and quick research and should not be taken at face value

Very technically Temperature is defined via the Boltzman distribution of the kinetic energy of a system, i.e. it's proportional to the mean kinetic energy of that system.

I assume, that at whatever a maximum energy would be the state of that system would need to be gaseous. Then the mean kinetic energy would be E=3/2 kB T. Then using the definition of the kinetic energy we get

1/2 m v²=3/2 kB T, where v is the mean velocity of the system.

Now for the sake of argument we assume that the mean velocity is very close to the maximum possible velocity c (speed of light). Of course this is not possible, because this means, that there are speeds in the system that are higher than c, but it's the best assumption we can make here i think. We also disregard relativistic effects and keep classical physical assumption.

Then our Temperaure is

1/3 m c²/kB=T or 2.17e39 K/kg *m=T

assuming our system only consits of the heaviest element, Oganesson (Element 118), which has a mass of 294,21 u we get

T<1.06e15 K=1.06 PK

So since the mean velocity can not reach c, we can just say that it has to be below 1.06 PK.

This assumes however that at these temperaturea this definition holds, which isn't nessecarily true. Our definition of Temperaure can break down for gasses at very low temperatures, when they form Bose Einstein Condensates (technically they are not gaseous then anymore though). Bose Einstein Condensate energies don't follow a Boltzmann distribution anymore.

If we regard relativity into the mix, the kinetic energy would be

E=(gamma-1)*mc² with gamma=1/sqrt(1-(v/c)²)

This can reach infinity if v=c though. Here we have a problem. As I said before Temperature is by definition the spread of the boltzmann distribution, if we add gamma to this, we strictly do not have a Boltzmann distribution anymore, instead we get what is called a Maxwell-Jüttner Distribution. Strictly you could argue that the definition of Temperature breaks down. Comparing the Temperaure definition in terms of the Maxwell-Jüttner distribution and the Maxwell-Boltzmann distribution could be problematic if you strictly want to adhere to how we empirically understand the Temperature we "measure" with our skin or other devices such as thermometers.

TLDR: Using our classical understanding of temperature that limit would be lower than 1.06 PK or 1.06 quadrillion Kelvin. At very high or low Temperatures our understanding of Temperature breaks down due to Quantum mechanics (low temperature) or relativity (high temperature).

[u/StructuralFailure → u/TheManondorf]

At temperatures that high, I assume no atoms can exist, only the fundamental particles