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Equation 23 · The Statistical Mechanics of Irreversibility at Molecular Scale

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Qmin⁡=kBTln⁡2Q_{\min} = k_{\mathrm B}T\ln 2

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Inputs and operationsk_mathrm BTln 2
Result or conditionQ_min
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Qmin⁡Q_{\min}

Symbol Q_min

the minimum heat dissipated to the environment.

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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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TT

Symbol T

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

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=

=

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

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subscript

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

Landauer’s analysis located a thermodynamic cost in logically irreversible operations. Resetting a one-bit memory from two equiprobable logical states to one standard state reduces its logical entropy. In an ideal isothermal implementation, the minimum heat dissipated to the environment is Qmin⁡=kBTln⁡2Q_{\min} = k_{\mathrm B}T\ln 2. per erased bit [ 9 ] . This is a lower bound on an idealized erasure, not a claim that every transistor switch dissipates exactly kBk_{\mathrm B}Tln⁡\ln2 , nor that computation in general has one universal energy per operation.

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