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⟨Δstot⟩≥0\left\langle \Delta s_{\mathrm{tot}} \right\rangle \ge 0

Why this formula appears here

Jensen’s inequality then gives ⟨Δstot⟩≥0\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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Δstot\Delta s_{\mathrm{tot}}

Symbol Δ s_tot

Δ sts_tot is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (1)

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⟨Δstot⟩≥0,\left\langle \Delta s_{\mathrm{tot}} \right\rangle \ge 0,

Equation 9 · Physics

The Statistical Mechanics of Irreversibility at Molecular Scale

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

Jensen’s inequality then gives ⟨Δstot⟩≥0\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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