Figure 7.

Entropy production rate at steady state, ${\dot{\sigma }}_{SS}$, against the number per cycle N by keeping the velocity v and diffusion coefficient D constant. Here, v (chosen to be $v=\frac{3D}{2\pi R}$) needs to be within the bound implied by $\beta \ge 0$ of Equation (38) for $N\ge 3$. (i) The blue circled line represents the entropy production rate in the continuous time limit $\Delta t\to 0$. (ii) The black squared line is the entropy production rate for a discrete time process using the maximal $\Delta t$ allowed by Equation (39), $\Delta t=-\frac{D}{v^2}+\sqrt{\frac{D^2}{v^2}+\frac{\Delta x^2}{v^2}}$.