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cianfa72

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- About the statistical thermodynamics analysis of the Feynman's brownian ratchet

Hi, as in a previous thread I would like to better understand the Feynman's analysis of brownian ratchet as described here:

https://www.feynmanlectures.caltech.edu/I_46.html

https://en.wikipedia.org/wiki/Brownian_ratchet

Consider the case in which the two boxes (i.e. heat baths) are at the same temperature ##T##.

The probability to gain the energy ##\epsilon## by a molecule hitting the paddle wheel is ##e^{-\epsilon/kT}##. What is at a given point in time the probability to turn forward the ratchet wheel?

https://www.feynmanlectures.caltech.edu/I_46.html

https://en.wikipedia.org/wiki/Brownian_ratchet

Consider the case in which the two boxes (i.e. heat baths) are at the same temperature ##T##.

The probability to gain the energy ##\epsilon## by a molecule hitting the paddle wheel is ##e^{-\epsilon/kT}##. What is at a given point in time the probability to turn forward the ratchet wheel?

In the above quote from Feynman 46-2, at first glance, the energy transformed in heat on the paddle wheel side should be ##\epsilon## and not ##\epsilon + L\theta##.The energy taken from the vane is ϵ+Lθ. The spring gets wound up with energy ϵ, then it goes clatter, clatter, bang, and this energy goes into heat. All the energy taken out goes to lift the weight and to drive the pawl, which then falls back and gives heat to the other side.

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