Predictive Maxwell's demons

Here we study the operation efficiency of a finite-size finite-response-time Maxwell's demon, who can make future predictions. We compare the heat and mass transport rate of predictive demons to nonpredictive ones and find that predictive demons can achieve higher mass and heat transport rates over longer periods of time. We determine how the demon performance varies with response time, future sight, and the density of the gasses on which they operate.

Figure 1

A schematic example illustrating the difference between a nonpredictive demon (top row) and a predictive (bottom row) demons, both with response time $\tau$. The nonpredictive demon decides on whether to open or close the gate based on tallying the desirable (green plus) and undesirable (red minus) particles within the present $\tau$ interval. In contrast, the predictive demon optimizes its open or close intervals globally, while still satisfying the constraint that the state of its gate cannot change faster than $\tau$. In this example, the nonpredictive demon generates a net current of one particle (three particles in the desired direction and two partiles in the undesired direction while the gate is open), whereas the predictive demon transports 4 particles within the same time.

Figure 2

Performance versus density. The performance of number demons (a) and energy demons (b) for predictive and nonpredictive (orange) cases are plotted as a function of right subsystem density, while the left subsystem density is kept constant (vertical dashed line), averaged over 500 particle arrival sequences.

Figure 3

Performance vs total time. Performance was average over 5000 random sets of events. (a) Predictive (blue) and nonpredictive (red) demons and their difference (green) is plotted for number (a) and energy demons (b).

Figure 4

Number and energy currents generated by predictive demons, as a function of response time. For all runs, the total time was $T=10$, and the time sight was $t_c=1$. (a) The performance of a number demon as response time changes. (b) The performance of the energy demon as response time changes.

Figure 5

Number demon performance, varying response time and time sight. The systems had parameters ${\rho }_l=50,{\rho }_r=100$. (a) Number rate vs response time for several fixed time sights. An averaging of 500 runs with $t=1$ second was used. (b) Number rate vs time sight for several fixed response times. The best fitting functions of the form ${\dot{N}}_{\tau }\left(t_c\right)=a_{\tau }(1-e^{-{\lambda }_{\tau }{t}_c})$ for each $\tau$ are shown in gray.

Figure 6

Convergence of a number demon's performance as the number of microbins increases, normalized by the performance of a nonpredictive number demon. As $g\to \infty$, the discrete algorithm for the demon better and better approximates the continuous demon model. Clearly, the discrete algorithm with $g=50$ is a good approximation to the continuous case, as the score ratio has stabilized by that point.