A temperature below absolute zero: Atoms at negative absolute temperature are the hottest systems in the world. 

Summary:

On the absolute temperature scale, which is used by physicists and is also called the Kelvin scale, it is not possible to go below zero – at least not in the sense of getting colder than zero kelvin. According to the physical meaning of temperature, the temperature of a gas is determined by the chaotic movement of its particles – the colder the gas, the slower the particles. At zero kelvin (minus 273 degrees Celsius) the particles stop moving and all disorder disappears. Thus, nothing can be colder than absolute zero on the Kelvin scale. Physicists have now created an atomic gas in the laboratory that nonetheless has negative Kelvin values. These negative absolute temperatures have several apparently absurd consequences: although the atoms in the gas attract each other and give rise to a negative pressure, the gas does not collapse – a behavior that is also postulated for dark energy in cosmology. 
Full story. 

Temperature as a game of marbles: The Boltzmann distribution states how many particles have which energy, and can be illustrated with the aid of spheres distributed in a hilly landscape. At positive temperatures (left image), most spheres lie in the valley at minimum potential energy and barely move; they therefore also possess minimum kinetic energy. States with low total energy are therefore more likely than those with high total energy – the usual Boltzmann distribution. At infinite temperature (centre image) the spheres are spread evenly over low and high energies in an identical landscape. Here, all energy states are equally probable. At negative temperatures (right image), however, most spheres move on top of the hill, at the upper limit of the potential energy. Their kinetic energy is also maximum. Energy states with high total energy thus occur more frequently than those with low total energy – the Boltzmann distribution is inverted.

Credit: LMU and MPG Munich

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