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The passage around this formula

Jensen’s inequality then gives $\left\langle \Delta s_{\mathrm{tot}} \right\rangle \ge 0$. which is the ensemble second law. The derivation is compact, but the assumptions are not optional. One must define the reverse experiment correctly, include relevant reservoirs and boundary terms, and avoid silently replacing the full state with an observed projection. Apparent violations often diagnose missing variables or an incorrectly specified conjugate process rather than new thermodynamics.

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