  The fundamental energy cost of irreversible computing is given by the
Landauer bound of $kT \ln2$~/bit. However, this limit is only achievable for
infinite-time processes. We here determine the fundamental energy cost of
finite-time irreversible computing \er{within the framework of nonequilibrium
thermodynamics}. Comparing the lower bounds of energy required by ideal serial
and parallel computers to solve a problem of a given size in a given finite
time, we find that the energy cost of a serial computer fundamentally diverges
with increasing problem size, whereas that of a parallel computer can stay
close to the Landauer limit. We discuss the implications of this result in the
context of current technology, and for different degrees of parallelization and
amounts of overhead. Our findings provide a physical basis for the design of
energy efficient computers.
