Equation 21 · Part 5 · The Statistical Mechanics of Irreversibility at Molecular Scale

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\langle\Sigma_\tau\rangle=\langle\Delta s_{\mathrm{tot}}\rangle/k_{\mathrm B}

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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.

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The passage around this formula

A molecular clock or motor is useful not only when its average current is nonzero but when that current is sufficiently precise. Let $J_\tau$ be an integrated current observed for time $\tau$ , such as net molecular steps or transported ions. Define dimensionless mean entropy production $\langle$ $\Sigma_\tau$ $\rangle$ = $\langle$ $\Delta$ $s_{\mathrm{tot}}$ $\rangle$ / $k_{\mathrm B}$ . A canonical steady-state thermodynamic uncertainty relation has the form

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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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Sources cited in the article section

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