Contact: Ulrich Schneider

ulrich.schneider@physik.uni-muenchen.de

49-891-733-251-890

Max-Planck-Gesellschaft

## Boltzmann Distribution 2

**Caption:** 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 that are distributed in a hilly landscape. At positive temperatures (left image), as are common in everyday life, 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 (center 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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