The particle has no temperature. It's not possible to translate the energy or speed into a temperature. A well-defined temperature is only possible when dealing with random velocity distributions.

There are laws of quantum physics. This has attracted a lot of attention recently. When chaos prevails, the well-known rules of thermodynamics follow from quantum physics.

**Boltzmann said that everything is possible.**

Different locations and different speeds are allowed for individual particles in the air. Not every state is likely.

Prof. Iva Brezinova says that it would be possible for all the energy in this space to be transferred to one single particle. This is so unlikely that it won't be observed.

According to the rules of classical physics, the probabilities of different states can be calculated. The temperature can be read off from the probability distribution because it's only determined for a large amount of particles.

**The entire world is a quantum state.**

Problems are caused when dealing with quantum physics. The equations of quantum theory are so complex that even the best supercomputers in the world can't solve them.

In quantum physics, the individual particles can't be considered in their own way. Every billiards ball has its own trajectory and location at all times. There is no individuality to quantum particles, they can only be described in a single quantum wave function.

The entire system is described by a single large quantum state according to Prof. Burgdrfer. It was a puzzle for a long time how a random distribution should produce a temperature.

**There is a chaos theory.**

Chaos has been shown to be a key factor in the team's success. The team performed a computer simulation of a quantum system consisting of a large number of particles and one of a different type of particle that acts as a thermometer.

There is no well-defined temperature for each individual quantum wave function of the large system. If you measure the particle'svelocity from the single quantum state, you can find a distribution that matches the well-established laws of thermodynamics.

Iva Brezinova says that it depends on chaos. We can change the interactions between the particles on the computer to create either a completely chaotic system or a system that shows no chaos at all. The presence of chaos determines whether a sample particle shows a Boltzmann temperature distribution or not.

If the combined system of sample particle and heat bath behaves chaotically, it's quantum theory that makes the difference. The strength of the chaos is what determines how well this behavior fits the Boltzmann formula.

One of the first cases in which the interplay between three important theories has been rigorously demonstrated is here.

The research is in a journal.

More information can be found in the article "Canonical Density Matrices from Eigenstates of Mixed Systems". There is a DOI called 10.3390/e 24121740.