Imitating Chemical Motors with Optimal Information Motors

To induce transport, detailed balance must be broken. A common mechanism is to bias the dynamics with a thermodynamic fuel, such as chemical energy. An intriguing, alternative strategy is for a Maxwell demon to effect the bias using feedback. We demonstrate that these two different mechanisms lead to distinct thermodynamics by contrasting a chemical motor and information motor with identical dynamics. To clarify this difference, we study both models within one unified framework, highlighting the role of the interaction between the demon and the motor. This analysis elucidates the manner in which information is incorporated into a physical system.

Figure 1

Depiction of the Brownian ratchet template. A particle moves in a periodic potential of period $l$ against a force $F=2\Delta E/l$. The potential switches randomly between two configurations mediated by either a chemical reaction (chemical motor) or a demon (information motor). Spatial diffusion and potential switches induce $R\leftrightarrow L$ transitions at rates $r_{ij}$ and $q_{ij}$ ($i,j=R,L$), respectively.

Figure 2

Plot of the entropy production rates for the chemical motor, ${\dot{S}}^{(\mathrm{chem}\mathrm{mot})}$ [Eq. (4)], and the information motor, ${\dot{S}}^{(\mathrm{info}\mathrm{mot})}$ [Eq. (12)], as functions of the external force $\Delta E$ for $q_{RL}=1$ and $\Delta \mu =\ln [(1-ϵ)/ϵ]=1$.

Figure 3

Illustration of the information motor fed by a tape of two-state ($N$ and $S$) cells each initially in $N$ and separated by a time interval ${\tau }_2$ (upper figure). Each cell couples to the ratchet for a duration ${\tau }_1$ during which $F_S$ is quasistatically lowered from $f_0\to \infty$ to $f$ while the reactions $R+S\leftrightarrow L+N$ and $R+N+A\leftrightarrow L+S+B$ individually evolve in a time-dependent free energy landscape (lower figure).