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Match of simulations to equilibrium thermodynamics

The graphs below show piston locations versus time for the thermalized experiments. (The time coordinate in the preceding movies goes up to 350.) Graphs 2, 4, and 5 are all for the case where the piston has mass 1. Other Graphs have piston mass 10. Graphs 5 and 10 are controls where the driver does not touch the piston. Graphs 12, 14, and 16 are the two-driver cases. Graphs 4, 9, and 14 use the expanding funnel shape; 16 has a triangular shape, so volume goes as x^2. The graphs give the impression, as expected, that (1) lots more work is extracted when there are two drivers; (2) slightly more work is extracted when we have the funnel shape.

Histograms of piston coordinate (simulations)
images/histo The force on the piston is 0.1, so each step of 10 on the horizontal scale corresponds to a work done of kT.
Histograms of piston coordinate at equilibrium (theory)

The problem with doing work against a constant force is that the maximum mechanical work that can ever be done by two particles expanding in a three-dimensional volume is 6kT -- well short of the 15kT achieved by a single ATP hydrolysis. Most of the available free energy is dissipated as heat during a irreversible burst of expansion from small x.

On the next page, we show how the amount of mechanical work done can be massively increased by matching the mechanical potential to the entropic potential.

Site last modified Tue Jul 5 12:32:01 BST 2005