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  "body": "\n## Summary\n\nA Gibbs measure is a probability measure in which the weight of a configuration is proportional to $e^{-\\text{energy}}$.\nIt comes from statistical mechanics, where it describes a system in thermal equilibrium.\nIn dynamics, the thermodynamic formalism uses Gibbs measures on [[shift spaces|A1XE59ZHNM]].\nThere the measure of a cylinder of length $n$ is comparable to the exponential of a Birkhoff sum of a potential.\nFor a Hölder potential on a mixing [[subshift of finite type|624XDXX8FN]] the Gibbs measure is unique and is the equilibrium state of the potential.\n\n## Explanations\n\n### L1 human\n\nImagine a long row of coins, and give each possible row an energy.\nA Gibbs measure picks rows at random so that low-energy rows are more likely, with odds given by the exponential of minus the energy.\nIn dynamics the \"row\" is the sequence of regions an orbit visits, and the energy is the sum of a function along the orbit.\nOn the full shift on two symbols, when the function is constant, every block of $n$ symbols gets the same weight, and one gets fair coin tossing.\n",
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