Heat production and information erasure. Of course, ordinary computers do not dissipate heat only when they erase information, but rather every time they change the voltage on a circuit node, even if the information stored on that node is also being kept elsewhere. But actually, in such a case, dissipating heat is not necessary to change the node's voltage. The node voltage can instead be changed by connecting the node to a charge supply line that is already at the same voltage, and then gradually ramping up the voltage on the supply line to the desired level. If the ramping is gradual, then arbitrarily little energy will be dissipated in this "abiabatic" charging operation.
If one uniformly follows the rule that a transistor is never turned on when there is a voltage between its source and drain, then this guarantees that the circuit is reversible, since there is no way to erase information in a circuit other than by equalizing voltage levels through a switch.
One might think that this rule makes general purpose computation impossible, but this is not so. Reversible logic theorists such as Fredkin and Toffoli showed long ago that any arbitrary logic function can be composed out of purely reversible primitives. More recently, Younis and Knight showed how to build efficient pipelined logic circuits in pure reversible fashion [Split-level Charge Recovery Logic].
Thanks to Roger Slykhouse rslykh@pacific.net.sg for pointing out the gap in the original discussion.