The Second Law, Maxwell's Demon, and Work Derivable from Quantum Heat Engines

With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.

Figure 1

For the cavity in contact with a heat sink at $T_2$, the accessible probability at all times, given a particular initial probability, is bounded in the area under the diagonal, with its reflection shown in gray above the diagonal. The other bounded area above the diagonal is for the cavity in contact with a heat bath at $T_1=T_2({\Delta }_1/{\Delta }_2)$.

Figure 2

Similar to Fig. 1 but this time with $T_1>T_2({\Delta }_1/{\Delta }_2)>T_2$. The maximum work can be extracted in a single cycle is proportional to the length of the vertical double arrow.