  Biomolecular machines transduce free energy from one form to another to
fulfill many important roles inside cells, with dissipation required to achieve
directed progress. We investigate how to break time-reversal symmetry at a
given dissipation cost by using deterministic protocols to drive systems over
sawtooth potentials, which have frequently been used to model molecular
machines as ratchets. Time asymmetry increases for sawtooth potentials with
higher barriers and for driving potentials of intermediate width. For systems
driven over a sawtooth potential according to a protocol, we find that
symmetric sawtooths maximize time asymmetry, while earlier work examining
ratchet models of molecular machines required asymmetric sawtooth potentials to
achieve directed behavior. This distinction arises because deterministically
driven machines are externally provided with direction, while autonomous
machines must generate directed behavior.
