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  "body": "\n## Summary\n\nThe Boltzmann equation describes a dilute gas through the density $f(t, x, v)$ of particles at position $x$ with velocity $v$.\nParticles move freely in straight lines and change velocity only in binary collisions, which the collision operator accounts for.\nIt links the motion of individual molecules with the equations of fluid dynamics.\nBoltzmann's H-theorem shows that a certain entropy cannot decrease, which explains the approach to equilibrium.\n\n## Explanations\n\n### L1 human\n\nA gas consists of a huge number of molecules flying around and bumping into each other.\nInstead of following each molecule, one keeps track of how many molecules are near each point with each velocity.\nBetween collisions this distribution just drifts along with the molecules.\nCollisions reshuffle velocities but keep the total momentum and energy.\nOver time the gas settles into the Maxwell distribution, the bell-shaped spread of velocities of a gas at rest at a fixed temperature.\n",
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