Well merging
This page is about …
- … energetic losses being incurred when potential energy wells of a bi-stable system are merged.
- … changing the state of a system without needing to expend energy (in the limit of slow speeds).
Contents
Contexts
Logic / computation
Changing bits from 0 to 1 or vice versa losslessly in reversible logic
possibly nanomechanical computation like e.g. rod logic.
Building & Energy
Depositong an atom from a tooltip to a workpiece losslessly.
Breaking and forming chemical bonds losslessly in a chemomechanical converter system.
The basic process to avoid well merging
Green arrows in graphic.
(1) While the barrier is still up
– Bring the occupied state in an energetic favorable
– Bring the unoccupied state in an energetic infavorable state
(2) Remove the barrier
– either bringing the wells closer together if a space of vacuum is the barrier (mechanosynthesis)
– or removing/retract a physical part responsible for the barrier (reversible logic)
This process may recuperate energy back into storage.
With absence of a barrier now an intermediate state is occupied.
(3) While the barrier is still down
– Bring the eventually to be occupied state in an energetic favorable
– Bring the eventually to be unoccupied state in an energetic infavorable state
(4) Raise the barrier
By doing step (2) in reverse.
Now the occupied state switched the well.
The barrier needs to be >>kT to prevent thermally caused flips.
Note that at no point there was this >>kT energy dissipated.
This would have happened if the barrier would have been removed
during a phase where the occupied state is in an well that is energetically unfavorable (or even equally favorable).
'Note that the process for reversible mechanosynthesis follows the very same principle. Just that …
– The green arrows are mapped to "reversible time".
– The barrier is removed by moving one well closer keeping the other one stationary. Matter of perspective.
– The favorability/unfavorability of wells could be influenced by angle of approach or offset of approach.
Well merging
The red arrows in the graphic shows these adiabatic process violations.
All these lead to irreversible energy dissipation.
This energy dissipative process is called "well merging".
In computation some times it is much more practically to strategically delete a few bits
by well merging rather than trying to keep absolutely everything reversible.
Fascinatingly if fully reversible logic would be exactly as powerful as irreversible logic then
cryptography based on asymmetric problem difficulty would be kind of broken.
See: Reversible logic
Coverage in the Nanosystems book
Page 186 Chapter 7.6. Transitions among time-dependent wells.
Figure 7.9. Merging of … wells
(wiki-TODO: Summarize Nanosystems findings here too.)
Limits to losslessness
Of course this is all merely near losslessly.
As there are are other dissipation mechanisms like dynamic friction
and dissipation pertaining to reciprocative motions.
Plus there is an absolute minimum amount to dissipate to define a local arrow of time for the nanomachinery.
Preventing it from running backwards occasionally.
Remaining dissipation in the adiabatic case
Regarding the absolute minimum energy needed for a system to operate forward at finite nonzero speeds:
This is a matter of dissipating enough energy per time to gain a sufficiently defined arrow of time.
In the context of chemomechanical converters, mechanochemistry and mechanosynthesis
a way to get down to the absolute minimum mandatory amount of energy dissipation may be
there process defined on the page dissipation sharing.
