Equation 9 · The Statistical Mechanics of Irreversibility at Molecular Scale
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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol Δ s_tot
Δ ot is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
change
Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
Jensen’s inequality then gives . 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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