The above analysis may be incorrect... there may be no limit to the amount of computation that can be done with a given finite amount of energy.
The late Nobel laureate Richard Feynman became very interested in the subject of computation and physics towards the end of his life. My understanding is that he concluded that there was no apparent limitation to the amount of computation that could be completed with a given amount of free energy. Computation may indeed always dissipate energy, but Feyman's conclusion was that this dissipated energy can be made arbitrarily small -- that there is no fundamental quantum limitation on the amount of computation that can be performed at any given mass-energy scale. The kT per logical operation can always be reduced to finer and finer scales. Presumably, this would require advances to ever new technologies, based on new physical forces that are relevant at finer scales (down to computation based on the interactions of quarks as in QCD, gravitons, etc.) Of course, since I can't give you references, you have to take this with a brick of salt... can anyone else comment on whether they have heard this about Feynman's conclusions?
Hi Doug, If you will check in the cumulative index for SciAm you will find several articles on this topic (which include references to headier stuff). Take care.