I have to say Nelsons use of analogies in this chapter seems overly complicated, such as his introduction of the G and S-ratchets.
So in order to understand his analogy I propose to consider a different analogy. Instead of a rod moving through a membrane driven by thermal fluctuations; take a simple chemical reaction.
A + B <-> C + D
The reaction can move either left or right. There is only a small difference in energies which can easily be supplied by thermal fluctuations.
The equilibrium can become biased when the activation energy for the products becomes large. In this way the amount of product will increase and reactant decrease (like the sliding of the rod).
By simply removing amounts of the product (Le Chatelier’s Principle) the reaction will keep forming products and use up the available reactants (like applying a force on the rod).