Entropy production in a photovoltaic cell

We evaluate entropy production in a photovoltaic cell that is modeled by four electronic levels resonantly coupled to thermally populated field modes at different temperatures. We use a formalism recently proposed, the so-called multiple parallel worlds, to consistently address the nonlinearity of entropy in terms of density matrix. Our result shows that entropy production is the difference between two flows: a semiclassical flow that linearly depends on occupational probabilities, and another flow that depends nonlinearly on quantum coherence and has no semiclassical analog. We show that entropy production in the cells depends on environmentally induced decoherence time and energy detuning. We characterize regimes where reversal flow of information takes place from a cold to hot bath. Interestingly, we identify a lower bound on entropy production, which sets limitations on the statistics of dissipated heat in the cells.

Figure 1

A quantum heat engine with near-degenerate ground states $|1\rangle$ and $|2\rangle$, and excited states $|h\rangle$ and $|c\rangle$, that resonantly (with frequency ${\omega }_l$) is coupled to two large heat baths kept at temperatures $T_c$ and $T_h$. Typical occupation probabilities are represented in green.

Figure 2

Incoherent (red) and coherent (blue) entropy flows in a hot (probe) environment versus cold-bath temperature $T_c$ for (a) two different values of decoherence time ${\tau }_2=5$ (dotted) and 10 (solid) and the absence of detuning energy. (c) Two different values of detuning $\delta /E_{h1}=0$ (dotted) and 7% (solid) both for the case of longer detuning time ${\tau }_2=10$. (b,d) The corresponding $p_1,p_2,p_c,p_h$ (black) and $-\text{Re}{\rho }_{12}$ (red) with the same order for dotted and solid lines. Other parameters are $E_h=1.5,E_c=0.4,E_1=E_2=0.1,T_h=\mathrm{\Omega }/2=n_l={\tilde{\chi }}_{h1}={\tilde{\chi }}_{h2}={\tilde{\chi }}_{c2}=10{\tilde{\chi }}_{c1}=1$.