  It is now well established that there is no lower bound for the energy
dissipated during a computation. The relevance of the zero-energy limit is
unclear, however, because it entails computations that are unreliable or
infinitely slow, or both. In contrast the thermodynamic costs of deterministic
computations that complete in finite time is less well understood. We propose a
model of universal computation based on Markovian stochastic processes. While
strictly deterministic computation is not possible in such systems, we show
that the scaling of the energy consumption in relation to the accuracy of the
computation is benign. This enables quasi-deterministic computation at modest
cost in energy and completing within finite time.
