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Equation 21 · Part 4 · The Statistical Mechanics of Irreversibility at Molecular Scale

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⟨Στ⟩=⟨Δstot⟩/kB\langle\Sigma_\tau\rangle=\langle\Delta s_{\mathrm{tot}}\rangle/k_{\mathrm B}
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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 JτJ_\tau be an integrated current observed for time τ\tau , such as net molecular steps or transported ions. Define dimensionless mean entropy production ⟨\langleΣτ\Sigma_\tau⟩\rangle=⟨\langleΔ\Delta stots_{\mathrm{tot}}⟩\rangle/kBk_{\mathrm B} . A canonical steady-state thermodynamic uncertainty relation has the form

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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