# Limit of hotness!

We know that there is a limit to which an object can be cooled down that is absolute zero, and getting there is also not very easy we may have to wait infinite years to get to that point. But is there any limit to how hot can any object get, or,

What is the hottest temperature it can reach in the universe, and how can this temperature be maintained?

I did some research and found that hottest temperature we have ever recorded is by the collision of gold atoms in Large Hadron Collider (LHC), that was 40000000000255.375 K !!! (that is ridiculously hot), but it was for a really short time. How can this extreme temperature be maintained for a significant amount of time?

• What is Farenheit... ? – ProfRob Dec 22 '14 at 20:36
• BTW I do know, it's just a long time since I've seen it in a scientific context. – ProfRob Dec 22 '14 at 20:44
• It's depends how long is "significant amount of time". For example, its currently believed what Big Bang was that hot: i0.wp.com/www.nikhef.nl/~i93/img/universe_original.jpg – Free Consulting Dec 23 '14 at 5:01
• 4...255.375 K? They measured that on exact on milli-Kelvin? Do you have a source for that? – Thomas Weller Aug 16 '19 at 0:22

I'm going to assume two things. (I) That we are tarking about a material/object at least in local thermodynamic equilibrium, otherwise it is difficult to give much physical meaning to the temperature. (II) That when you say "we can produce" I take that (on Astronomy SE) to mean "we can observe or deduce".

The obvious winner, in the sense that we can still "observe" what happened (the outcome) is from the first fraction of a second of the universe. The electroweak transition occurred at temperatures of around $10^{15}$K and left us with the weak force, electromagnetic force, baryon masses and possibly the matter/anti-matter asymmetry.

The production of helium and lithium in the universe took place at temperatures of $>10^{10}$K and we can still see the evidence.

Neutrinos are produced copiously in the cores of supernovae at temperatures of $10^{11}$K. These neutrinos have been observed from Supernova 1987A.

• So the place where neutrinos are produced is much hotter than collision of gold atoms. – Dheeraj Kumar Dec 23 '14 at 3:18

Perhaps more fundamentally than temperature, the 'hotness' or 'coldness' of a system can be described by the thermodynamic beta instead, which just like temperature is determined by the rate of change of entropy with respect to energy (at constant volume and particle number): $$\beta\equiv\frac{1}{k_\text{B}}\left.\frac{\partial S}{\partial E}\right|_{V,N}\!\!=\frac{1}{k_\text{B}T}\text{.}$$ Intuitively, the thermodynamic beta measures the coldness of a system from $-\infty$ to $+\infty$. Since temperature per se is just the reciprocal of $\beta$, up to a factor of Boltzmann's constant $k_\text{B}$, that means the coldest is at $T\to 0^+$, approaching zero from positive temperature side, while the hottest is $T\to 0^-$, from the negative. Treating $+0\,\mathrm{K}$ as different from $-0\,\mathrm{K}$ may seem bizarre, but that's what we get for taking a reciprocal.

Negative temperatures ($\beta<0$) are hotter than any positive temperature ($\beta > 0$). They can happen when a system has more high-energy states occupied than low-energy states, such as during population inversion of any laser, or during similar astrophysical phenomena.

• There is an excellent video by Sixty Symbols on this topic. – Arne Dec 23 '14 at 6:49