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:
cf The first 15600 time units when both piston and driver are thermalized (as on the previous page) Another detail shot from the "driver-thermalized, only" simulation: 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)