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  "body": "\n## Summary\n\nA caloric function is a solution of the [[heat equation|VP2HN86VAG]] $\\partial_t u = \\Delta u$ on an open set of space-time.\nCaloric functions play for the heat equation the role that [[harmonic functions|0DEB0JMN0W]] play for the Laplace equation.\nMuch of classical potential theory, such as mean value formulas, maximum principles and the Perron method, has a parallel version for caloric functions.\nThis parallel theory is often called parabolic or caloric potential theory.\n\n## Explanations\n\n### L1 human\n\nThink of $u(x, t)$ as the temperature at the place $x$ at the time $t$ in a body where heat simply spreads out.\nA caloric function is any temperature profile that obeys the law of heat flow.\nA harmonic function that does not depend on time is caloric, since it describes a steady temperature.\nA simple example in one space variable is $u(x, t) = x^2 + 2t$: here $\\partial_t u = 2$ and $\\partial_x^2 u = 2$.\nAnother is $u(x, t) = e^{-t} \\sin x$, a wave of heat that fades as time goes on.\n",
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