"It is argued that computing machines inevitably involve devices which perform logical functions that do not have a single-valued inverse."As we've heard, and as we'll see in detail, Bennett showed in 1973 that this is not the case. Landauer's next sentence in the abstract is the key result so often cited:
"This logical irreversibility is associated with physical irreversibility and requires a minimal heat generation, per machine cycle, on the order kT for each irreversible function."
The main argument occurs on p. 187; the rest of the paper provides some scaffolding and heuristic support for the general contention about the energy cost of logical irreversible and the physical consequences. The gist is that if we halve the number distinguishable states by erasing a bit (resetting to 1, say), then Delta Q = -T*Delta S = -k*T*ln(2), and that this decrease in entropy must be dissipated elsewhere in the universe as heat.
How much energy is k*T*ln(2)? Well, about 2.87*10^{-21} joules, or watt-sec. A 60-watt bulb then uses an amount of energy equivalent to the lower bound on the cost of erasing about 20 billion Terabits/sec.
Note that some of the algebra is a bit hard to follow and has at least one typo, but we're straighten that out.