  Landauer's Principle that information loss from a computation implies entropy
increase can be rigorously proved from mathematical physics. However, carefully
examining its detailed formulation reveals that the traditional identification
of logically reversible computational operations with bijective transformations
of the full digital state space is actually not the correct logical-level
characterization of the full set of classical computational operations that can
be carried out physically with asymptotically zero energy dissipation. To find
the correct logical conditions for physical reversibility, we must account for
initial-state probabilities when applying the Principle. The minimal
logical-level requirement for the physical reversibility of deterministic
computational operations is that the subset of initial states that exhibit
nonzero probability in a given statistical operating context must be
transformed one-to-one into final states. Thus, any computational operation is
conditionally reversible relative to any sufficiently-restrictive precondition
on its initial state, and the minimum dissipation required for any
deterministic operation by Landauer's Principle asymptotically approaches 0
when the probability of meeting any preselected one of its suitable
preconditions approaches 1. This realization facilitates simpler designs for
asymptotically thermodynamically reversible computational hardware, compared to
designs that are restricted to using only fully-bijective operations such as
Toffoli type operations. Thus, this more general framework for reversible
computing provides a more effective theoretical foundation to use for the
design of practical reversible computers than does the more restrictive
traditional model of reversible logic. In this paper, we formally develop the
theoretical foundations of the generalized model, and briefly survey some of
its applications.
