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Equation 3 · The Arrow of Time and the Engine of Evolution

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kBTk_{\mathrm{B}}T

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kBk_{\mathrm{B}}

Symbol k_B

kBk_B is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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TT

Symbol T

the temperature.

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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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Charles Bennett used Landauer’s bound to close a hole that had troubled physicists since Maxwell first imagined a demon who could sort fast and slow molecules without doing work. Bennett’s 1982 review argued that a demon can, in principle, measure a molecule’s state without inevitable dissipation — measurement per se can be made close to thermodynamically reversible if implemented carefully. What the demon cannot do is remember indefinitely: with a memory of finite capacity, a demon that keeps operating must eventually erase old records to make room for new ones, and it is that erasure, governed by Landauer’s bound, that generates the entropy needed to save the second law [ 4 ] . Bennett’s…
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Charles Bennett used Landauer’s bound to close a hole that had troubled physicists since Maxwell first imagined a demon who could sort fast and slow molecules without doing work. Bennett’s 1982 review argued that a demon can, in principle, measure a molecule’s state without inevitable dissipation — measurement per se can be made close to thermodynamically reversible if implemented carefully. What the demon cannot do is remember indefinitely: with a memory of finite capacity, a demon that keeps operating must eventually erase old records to make room for new ones, and it is that erasure, governed by Landauer’s bound, that generates the entropy needed to save the second law [ 4 ] . Bennett’s same 1982 paper makes a striking, and often overlooked, quantitative aside relevant to biology directly: he estimated that the cellular machinery of DNA replication, transcription, and translation behaves like nature’s closest real approximation to a “Brownian computer” — a device that lets thermal noise drive it through its operations rather than forcing them ballistically — and that this machinery dissipates on the order of 20 to 100 kBk_{\mathrm{B}}T per elementary step [ 4 ] . That number sits far above Landauer’s idealized floor, exactly as Bennett’s framework predicts it should for a real, imperfectly optimized molecular process, and it previews a theme the rest of this article returns to: heredity is a record-keeping technology, genomes are memory, and every act of retaining one variant over another is, physically, the same kind of erase-and-rewrite operation Bennett’s demon performs, paid for out of the same thermodynamic ledger.

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