CIS 4930.1194X/6930.1078X Spr.'00
Week 2 Assignment:
Thermodynamic limits and other misc. physics issues

Please continue to follow the general advice on reading assignments from last week's assignment.

Reading assignment:

Lecture 5: Reversibility & the 2nd law of thermo.:

This lecture introduces the concepts of the reversibility of physics, the second law of thermodynamics, the thermodynamic cost of information erasure, and the essential ideas of reversible computing.

With some of the following items we are getting a little ahead of ourselves and anticipating our later, more detailed study of reversible computing (part 7 of the course, in the final 3 weeks). But this material ties in to today's topic and gives you a little of the flavor of what we'll be doing later.

These first two items are a survey of this subject.  I would like everyone to please at least read section 2.5 of my thesis (the green book).

The following two articles are by the pioneers of the thermodynamics of computing. This next article is a detailed analysis of superconducting logic elements showing that they can dissipate less energy than the characteristic thermodynamic and quantum energies kT and hf. Lecture 5+i: Chaos, analog computing, general relativity:

I am not going to give a full lecture on this topic, because the upshot of what I would say is just to argue that the limited entropy of bounded systems (implied by quantum mechanics) means that no physically-implemented form of chaotic or analog computation can possibly have greater computational power than ordinary digital forms of computation.  (Although we will see later in the course that digital quantum computation does apparently have greater power.) Physics appears to make our universe fundamentally digital, not analog, for computational purposes.  However, if you're interested in learning more about analog computation concepts, and in seeing the pro and con arguments in more detail, here are some helpful readings:

A fairly good review:

This next paper by Smith discusses a result that idealized Newtonian mechanics seems to say that infinite computation can be done by a system in finite time (with kinetic energies asymptotically approaching infinity).  Of course, the ideal Newtonian model is not physically realistic, as Smith demonstrates using the more correct, general-relativistic model of gravity. Siegelmann's dissertation research (summarized in this Science article) was to show that certain analog systems have greater computational power than Turing machines.  However, again I would argue this statement has zero practical value because these models are not physically realizable; no real physical system can embody the unbounded amounts of information that are required in order to attain the extra power. In this next article, Smith analyzes another model of analog computers ("plane mechanisms") that have sometimes been claimed to have greater computational power (in the sense of exponentially greater efficiency) than ordinary digital computers, and he again argues that no real physical instantiations of them would actually have such power. Additional background material:

Nothing special for this week. If you start to feel lost on something, and you want to fix the problem, ask me for more background reading material and I'll try to help you out.

Written assignment: (due Mon. 1/24)

This is the same as last week's written assignment, except that it should be on the subject of this week's lectures and reading material, and it's due next Monday. You might want to review the available options; I added a new one (dispute the material) since the list was first written.

If you wish, you can also write about the material on quantum limits, since some of it spilled over from last week to this week.