Figure 2.

Entropy production rate at steady state $\dot{\sigma }(t\to \infty )\equiv {\dot{\sigma }}_{SS}[=-{\dot{S}}_e]$ against the number of sites N per cycle by keeping the velocity v and diffusion coefficient D constant. The velocity v (here chosen to be $v=\frac{3D}{2\pi R}$) needs to be within the bounds implied by $\beta \ge 0$ of Equation (13) for $N\ge 3$. The red line is the entropy production rate in the limit $N\to \infty$ and takes the value ${\dot{\sigma }}_{SS}(N\to \infty )=v^2/D$.