The Failure of the Thermodynamics of Computation (2010)

John D. Norton

Center for Philosophy of Science

Department of History and Philosophy of Science

University of Pittsburgh

Revised and improved edition, July 2013.

The thermodynamics of computation seeks to identify the principled thermodynamic limits to computation. It imagines computations carried out on systems so small that their components are of molecular sizes. The founding tenet of the analysis is that all the processes excepting one can in principle be carried out in a non-dissipative manner, that is, in a manner in which no thermodynamic entropy is created or passed to the surroundings. The sole class of necessarily dissipative processes is identified by the central dogma as those physical processes that implement a logical, many-to-one mapping. The universal example of such a process is erasure. It takes a memory device that may be in many different states and maps it to one, a single reset state.

Elsewhere I have argued that the thermodynamics of computation is gravely troubled. Its leading principle, Landauer's Principle, connects erasure to entropy dissipation. Yet there is still no sound justification for it. The proofs that have been given rest on fallacies or misapplications of statistical and thermal physics. The purpose of this site is to describe a different problem in the theory that I hope will be of more general interest in philosophy of science. It gives a concrete example of what can go wrong if one uses idealizations improperly.

An ineliminable assumption of the thermodynamics of computation is that one can employ a repertoire of non-dissipative processes at molecular scales. These processes are thermodynamically reversible and, if carried out, would involve no net creation of entropy.

All thermal processes at molecular scales are troubled by fluctuations. They arise because thermal processes are the average of many microscopic molecular processes and the averaging is never quite perfect. Most famous of these is the Brownian motion that leads pollen grains to dance about under a microscope. The dancing arises because the collisions with the pollen grain of water molecules from all sides do not quite average out to leave no effect.

My contention here is that the reversible processes presumed in the thermodynamics of computation are fatally disrupted by fluctuations that the theory selectively ignores. That is especially awkward since the one occasion on which processes connected to fluctuations are not ignored is when the theory treats the thermodynamics of erasure.

As a result, the founding tenet of the thermodynamics of computation--that erasure-like processes only are necessarily dissipative--arises entirely because fluctuations have been idealized away selectively for other processes. In short the basic conception of the theory itself derives from inconsistently implemented idealizations.

Idealizations are a routine part of science. They are known falsehood, sometimes introduced for theoretical convenience or sometimes out of necessity. The latter arises often in physics, since no theory gives the complete truth. Every theory is an idealization to some degree.

When used wisely, idealizations enable good physics. Galileo was able to develop his theory of projectile motion precisely because he idealized away air resistance. It is the classic case of successful idealization. Their imprudent use, however, can lead to great mischief. Imagine that one tries to give an account of airplane flight that neglects the effect of air passing over the airplane. It is the same idealization as used by Galileo. However now it leads to the disastrous result that sustained flight is impossible for an airplane.

My goal here is outline a striking case of a bad idealization in present science. It has created a spurious science, known as the "thermodynamics of computation." The analyses in this science are dependent upon idealizing away thermal fluctuations in an arbitrary and selective manner. If one treats the fluctuations consistently, the results of the science disappear.

One can get an idea in advance of what the problem will be by thinking about scaling. We tend to imagine things remaining pretty much the same as we scale things down. If we were one tenth or one hundredth our size, we imagine that that we could carry on our business pretty much as normal, as long as everything else was scaled down correspondingly. Famously, those intuitions are flawed.

When we scale static objects down to molecular sizes, we imagine that they will stay put, just as they did at macroscopic scales. At the larger scale, it is no great feat to stack up a few children's blocks. But if they were scaled down to molecular sizes, the accumulated impact of air molecules on the now minuscule block would not average out smoothly. The block would be jumping about. Simple stacking and all the other building processes that we take for granted at larger scales would be fatally disrupted.

The thermodynamics of computation has proceeded by assuming too often that one can scale down to molecular sizes familiar processes that work well on macroscopic scales. The ones that do not scale down are the non-dissipative processes, for they can be non-dissipative by virtue of being in perfect but delicate equilibrium at every stage. The thermal fluctuations that lead tiny block to jiggle about will disrupt them as well.