Thermodynamic Bounds on Efficiency for Systems with Broken Time-Reversal Symmetry

We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a “figure of merit” and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have Carnot efficiency and nonzero power simultaneously .

Figure 1

Schematic drawing of the model.

Figure 2

Function $h(x)$ (blue solid curve). This function has a vertical asymptote at $x=1$ (dashed line). Thermodynamics restricts the parameter $y$ between $y=0$ and $y=h$.

Figure 3

Ratio $\eta /{\eta }_C$ as a function of the asymmetry parameter $x$, with $\eta ={\eta }^{\star }$ (dashed curve) and $\eta ={\eta }_M$ (solid curve). The black filled circle corresponds to the Curzon-Ahlbohrn limit at $x=1$: ${\eta }_{\mathrm{CA}}^{(l)}={\eta }_C/2$.