Algorithmic complexity and efficiency of a ratchet

Molecular motors are characterized by a high degree of efficiency of energy transformation in the presence of thermal fluctuations. A fundamental question is how the efficiency of thermal ratchets depend on temperature and the flow of physical information (or negentropy). In order to address this question, in this work we have calculated the algorithmic complexity (or Kolmogorov information entropy) of a smoothly varying potential ratchet. The complexity is measured in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. For a wide range of values of the flipping rate, the algorithmic complexity is found to be proportional to the efficiency in a flashing thermal ratchet. In addition, we find that at low temperatures, the algorithmic complexity (or efficiency) of a thermal ratchet increases with temperature. This is a highly counterintuitive result that may be important in the operation of molecular motors.