Recently, Ralph Merkle (of Xerox Parc) and I independently discovered a reversible formulation of electronic switch logic which makes it relatively straightforward to design reversible computers (or computers in which the destruction of information is limited and/or controlled) using simple extensions of conventional logic design techniques.
The biggest hitch to bootstrapping most of existing software technology onto reversible architectures appears to be floating point numbers. Integer and symbolic operations can be formulated so that logical irreversibility in the implementation occurs only when it occurs in the algorithm (for example, sorting is logically irreversible).
Parenthetically, it is of course always possible to make a process reversible by saving the bits that would be destroyed (and then perhaps running the process backward to erase the storage). I conjecture that in practice one would simply use a heat sink instead. Thus it is a matter of interest to reduce the number of bits that would have been written on the tape, or which are destroyed using the heat sink.
Now suppose we are simulating some physical process in which entropy increases, in the usual interpretation (e.g. mixing a hot and a cold fluid). There is of course an interpretation in which the entropy does not increase, since one starts and finishes in a single microstate. Yet the describable macrostate of the endpoint is much larger than that of the beginning.
Now consider that a vector of computer numbers, most likely floating point, will be used to approximate the system's microstate, and that these numbers are of limited precision. Thus one can approximate a system's track through phase space. But as tracks from adjacent representable points fan out, there will be representable intermediate points which should have as precursors non-representable points between those of the original set.
One could trade accuracy for reversibility. In the fanout, the true image of the original points will retain its volume in phase space, so the image of other precursor points will be ``mixed in''. One could arbitrarily map some points in the image area to each of the precursor sets. (In theory anyway. It seems a daunting task to perform in practice, given the number of states implied by, often, millions of bits of state information.)
Thus it seems to be a relatively intrinsic property of conventional
physical modeling techniques, that they will exhibit logical irreversibility
when simulating processes in which the entropy changes. Thus the simulation
will require an increase in entropy (with all the above interpretations
and provisos). Given that the phase space can have a fractal structure,
so that there is no resolution of simulation that is fine enough to avoid
the ``aliasing'' problems, it may be that (wild-eyed conjecture:) there
is a fineness of simulation at which the computer must undergo the same
entropy increase as the process being simulated.