# Breaking time-reversal symmetry for ratchet models of molecular machines

## TL;DR

This paper explores how to induce time-reversal symmetry breaking in molecular machine models using deterministic protocols over sawtooth potentials, revealing conditions that maximize asymmetry and contrasting externally driven versus autonomous systems.

## Contribution

It demonstrates how deterministic driving protocols can break time-reversal symmetry in ratchet models, highlighting the role of potential symmetry and driving parameters in molecular machines.

## Key findings

- Symmetric sawtooth potentials maximize time asymmetry under deterministic driving.
- Higher barriers and intermediate width driving potentials increase time asymmetry.
- Externally driven systems differ from autonomous ones in symmetry requirements for directed motion.

## Abstract

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.