Biomolecular motors are macromolecules of enzyme proteins that convert chemical energy into mechanical energy. Experimental studies have shown that the directed movement of the biomolecular motor fully participates in the material transport process in the cell. Theoretically, the directed movement of biomolecular motors can be studied by the ratchet model. However, in most of feedback control ratchet models, none of the influences of external factors on experimental manipulation is considered, especially the inevitable random error, systematic error and human error in the experiment. Therefore, in order to further study the influences of error factors on feedback control ratchets, Cao's research group (Feito M, Cao F J 2007 Eur. Phys. J. B 59 63) pioneered the idea of error probability and discussed the transport behavior of feedback ratchets in the presence of error probability.

Based on Cao's error ratchet model, in this paper the temperature factor in introduced to further control the feedback ratchets, and the directed transport characteristics of the coupled Brownian particles in the temperature feedback ratchets are studied. The effects of temperature factor, phase difference and temperature frequency on the directed transport of coupled Brownian particles are discussed in detail. It is found that the temperature factor does not always reduce the directed transport of Brownian particles. There is a minimum value which means that the temperature factor can enhance the directed transport of the feedback ratchets within a certain change interval. In addition, in a small temperature amplitude range, the directed transport of the coupled particles exhibits a multi-peak structure with the change of temperature frequency. It is means that the appropriate temperature change frequency can enhance the directed transport of the feedback ratchets multiple times. The conclusions obtained in this paper can not only inspire experimental selection of appropriate temperature feedback information to optimize the directed transport of the Brownian ratchets, but also provide theoretical references for analyzing and processing the experimental data, especially error analysis.