  Conventional computing has many sources of heat dissipation, but one of
these--the Landauer limit--poses a fundamental lower bound of 1 bit of entropy
per bit erased. 'Reversible Computing' avoids this source of dissipation, but
is dissipationless computation possible? In this paper, a general proof is
given for open quantum systems showing that a computer thermally coupled to its
environment will necessarily dissipate entropy (and hence heat). Specifically,
a lower bound is obtained that corresponds to the adiabatic regime, in which
the amount of entropy dissipated per computational operation is proportional to
the rate of computation.
