Fluctuation-response relation in a rocking ratchet. 
The relationship between the positional fluctuation and mechanical response for a thermal ratchet at a nonequilibrium steady state was investigated experimentally and considered theoretically.  We constructed a ratchet system using a scanning optical trapping system and microbeads (0.20 microm diameter), which is interpreted as a realization of a rocking ratchet [M. O. Magnasco, Phys.  Rev. Lett.  71, 1477 (1993)].  In the experiment, an asymmetric periodic potential (2.5 microm period) was generated by optical trap scanning, which traps a bead.  When the potential profile was rocked sinusoidally, diffusion of the bead was rectified in one direction.  We confirmed that both the diffusion coefficient and the mobility increased with potential rocking with a positive correlation.  To obtain better insight, we performed numerical and theoretical analyses of the corresponding Langevin system.  Although there is a positive relationship between the diffusion coefficient and mobility, the diffusion coefficient is greater than the value given in the Einstein relation.  This result means that the effective temperature of the thermal ratchet at a nonequilibrium steady state becomes greater than that of the environment.  We propose that this elevation of the effective temperature causes a decrease in the energetic efficiency of the thermal ratchet through irreversible dissipation to the heat bath.