How does the heat equation change in the real world?

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The heat equation traditionally suggests that heat disperses infinitely over time, but real-world conditions necessitate modifications. In practical applications, relativity must be considered, leading to an upgraded form of the equation that adheres to Lorentz invariance. This adjustment reflects the limitations of classical physics in accurately modeling heat transfer at high velocities. The discussion highlights the importance of integrating relativity into thermal dynamics for accurate predictions. Understanding these modifications is crucial for applying the heat equation in realistic scenarios.
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The heat equation predicts that heat spreads infinitely far over arbitrarily small time intervals. What happens in real life? How does the heat equation get modified?
 
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In the real (classical) world, you have to take into account relativity, which can be done by a well defined way of "upgrading" a Galileo-invariant equation to a corresponding Lorentz-invariant one. There is a relevant Wikipedia article you can read here: http://en.wikipedia.org/wiki/Relativistic_heat_conduction
 

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