The thermal (Boltzmann) distribution can be illustrated with balls distributed on a hilly landscape. The landscape provides both a lower and upper bound for the potential energy of the balls. At positive temperatures (left figure), common in everyday life, most balls lie in the valley around minimum potential energy. They barely move and therefore also possess minimum kinetic energy. States with small total energy are therefore more likely than those with large total energy — the usual Boltzmann distribution. At infinite temperature (central figure) the balls spread evenly over low and high energies in an identical landscape. Here, all energy states are equally probable. At negative temperatures (right figure), however, most balls wander on top of the hill, at the upper limit of potential energy. Also their kinetic energy is maximal. Energy states with large total energy are occupied more than those with small total energy — the Boltzmann distribution is inverted.
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