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Equation 9 · Part 3 · The Statistical Mechanics of Irreversibility at Molecular Scale

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

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

The passage around this formula

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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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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