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Wmax⁡=kBTln⁡2W_{\max} = k_B T \ln 2

Why this formula appears here

Szilard reduced Maxwell’s population of molecules to the simplest case that still carried the paradox: a single gas particle in a box. An external agent measures which half of the box the particle occupies, inserts a partition, and lets the particle push a piston on the side it occupies, converting the result of that one-bit measurement into extractable work. Szilard showed that the demon’s ability to extract work was tied exactly to the amount of information it acquired in the measurement — one bit of information corresponds to a definite quantity of work, kBk_B T ln⁡\ln 2 , where kBk_B is Boltzmann’s constant and T is the bath temperature. This is worth stating as an equation because it is the…

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Wmax⁡W_{\max}

Symbol W_max

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

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Wmax⁡=kBTln⁡2W_{\max} = k_B T \ln 2

Equation 4 · Physics

From Origins to Frontier: A History of Stochastic Thermodynamics and Complex Systems

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

Szilard reduced Maxwell’s population of molecules to the simplest case that still carried the paradox: a single gas particle in a box. An external agent measures which half of the box the particle occupies, inserts a partition, and lets the particle push a piston on the side it occupies, converting the result of that one-bit measurement into extractable work. Szilard showed that the demon’s ability to extract work was tied exactly to the amount of information it acquired in the measurement — one bit of information corresponds to a definite quantity of work, kBk_B T ln⁡\ln 2 , where kBk_B is Boltzmann’s constant and T is the bath temperature. This is worth stating as an equation because it is the…

Meanings in this article

  • TT: the bath temperature.
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