Equation 20 · The Statistical Mechanics of Irreversibility at Molecular Scale

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\tau

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\tau

Symbol τ

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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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