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

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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 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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Στ\Sigma_\tau

Symbol Sigma_τ

Sigma_τ is part of the quantity the equation computes from the expression on the right.

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Δstot\Delta s_{\mathrm{tot}}

Symbol Δ s_tot

Δ sts_tot is an input to the expression that computes the quantity on the left.

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kBk_{\mathrm B}

Symbol k_mathrm B

kmk_mathrm B is an input to the expression that computes the quantity on the left.

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Published contexts (1)

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

Equation 21 · Physics

The Statistical Mechanics of Irreversibility at Molecular Scale

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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