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The Hidden Second Law of Thermodynamics behind the Boltzmann-Grad Limit
We show that the Boltzmann-Grad (BG) limit, $N\varepsilon^{d-1}=α=\text{const}$, is not a neutral scaling condition but already encodes the Second Law of Thermodynamics, resolving Loschmidt's paradox. Newton's First Law is the bridge: applying the BG condition locally to two adjacent cells at differ
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