Found on John Baez’s weekly finds in mathematical physics:

K. Eric Drexler writes:

Dear John,

John Baez wrote:

> […] with a perfectly tuned dynamics, an analogue system
> can act perfectly digital, since each macrostate gets
> mapped perfectly into another one with each click of
> the clock. But with imperfect dynamics, dissipation
> is needed to squeeze each macrostate down enough so it
> can get mapped into the next - and the dissipation
> makes the dynamics irreversible, so we have to pay a
> thermodynamic cost.

Logically reversible computation can, in fact, be kept on track without expending energy and without accurately tuned dynamics. A logically reversible computation can be embodied in a constraint system resembling a puzzle with sliding, interlocking pieces, in which all configurations accessible from a given input state correspond to admissible states of the computation along an oriented path to the output configuration. The computation is kept on track by the contact forces that constrain the motion of the sliding pieces. The computational state is then like a ball rolling along a deep trough; an error would correspond to the ball jumping out of the trough, but the energy barrier can be made high enough to make the error rate negligible. Bounded sideways motion (that is, motion in computationally irrelevant degrees of freedom) is acceptable and inevitable.

Keeping a computation of this sort on track clearly requires no energy expenditure, but moving the computational state in a preferred direction (forward!) is another matter. This requires a driving force, and in physically realistic systems, this force will be resisted by a “friction” caused by imperfections in dynamics that couple motion along the progress coordinate to motion in other, computationally irrelevant degrees of freedom. In a broad class of physically realistic systems, this friction scales like viscous drag: the magnitude of the mean force is proportional to speed, hence energy dissipation per distance travelled (equivalently, dissipation per logic operation) approaches zero as the speed approaches zero.

Thus, the thermodynamic cost of keeping a classical computation free of errors can be zero, and the thermodynamic cost per operation of a logically reversible computation can approach zero. Only Landauer’s ln(2)kT cost of bit erasure is unavoidable, and the number of bits erased is a measure of how far a computation deviates from logical reversibility. These results are well-known from the literature, and are important in understanding what can be done with atomically-precise systems.

With best wishes,

Eric

For an introduction to Drexler’s plans for atomically-precise reversible computers, see:

28) K. Eric Drexler, Nanosystems: Molecular Machinery, Manufacturing, and Computation, John Wiley and Sons, New York, 1992.

The issue of heat dissipation in such devices is also studied here:

29) Ralph C. Merkle, Two types of mechanical reversible logic, Nanotechnology 4 (1993), 114-131. Also available at http://www.zyvex.com/nanotech/mechano.html

I need to think about this stuff more!

The upshot of this is that by running our minds on reversible molecular computers, we can live forever and expend no energy.

Anthropics alert: if this is so, why weren’t we born in the future era of infinite free computation and lifespan?

Answer: we still know practically nothing about the physical delineations of our reference class, so we can’t say what the probability distribution of our likelihood of birth looks like with much accuracy.

Read more on reversibility from Robin Hanson and anthropics from Milan M. Cirkovic.