D.J.C. MacKay and R.S. MacKay: Ergodic pumping: Nonlinear potentials

·	Summary

Abstract

Further observations
·	Hamiltonian models
·	Unequal masses
·	Multiple drivers
·	Thermalize
·	Changing shape
·	Two particles
·	Modified volume
·	Control experiment
·	Theory 1
·	Theory 2
·	Nonlinear potentials «
·	16kT of work
·	Movies
·	More results
·	Niggles
·	Simple One-D
·	More One-D
·	Yet More One-D
·	Charged exit-path trick
·	Complication with simulations
·	Discussion of 1-6 potential
·	Details
·	Pressure paradox
·	Useful numbers

Nonlinear potentials

U(x)=-B/4(x-x0)^4+C/6(x-x0)^6

U(x)=-A/(x-x0)+A'/6(x-x0)^6

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Predicted histograms of piston coordinate at equilibrium

Adding in a 4-6 potential to emulate dipole binding massively increases work done during the expansion: without 4-6 potential - about 4kT; with 4-6 potential - about 16kT illustrated here. [Probability densities are not accurately normalized.]

images/onesixtheory

Adding a 1-6 potential. The red curve shows the total free energy G(x) = U(x) - TS(x). Next page