D.J.C. MacKay and R.S. MacKay: Ergodic pumping: Yet More One-D

·	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

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More one-dimensional Hamiltonian simulations

On this page, another thermalization rule. In addition to the "wall-hitting" thermalizations, we thermalize the driver (but not the piston) every 1 time-unit. The marginal distribution of the piston coordinate and the marginal distribution of the driver coordinate should both be unchanged by this thermalization rule, though the autocorrelation times are strongly affected.
As confirmation of the validity of these simulations, predicted and actual histograms of the work done are shown at the end.
The first 2150 time units:
One Thermalized0.9.2150

cf The first 15600 time units when both piston and driver are thermalized (as on the previous page) images/BothThermalized0.9.15600

Another detail shot from the "driver-thermalized, only" simulation: One Thermalized0.9 detail

Predicted (yellow) and actual (red) histogram of work done; 200000 samples


Results when the driver is thermalized every 1 time units	Results when thermalization occurs only when the state reaches one of the state-space constraints (in fact, mainly when the driver reaches the left-hand wall)

David J.C. MacKay

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