Thermodynamics of Quantum Information Flows

We report two results complementing the second law of thermodynamics for Markovian open quantum systems coupled to multiple reservoirs with different temperatures and chemical potentials. First, we derive a nonequilibrium free energy inequality providing an upper bound for a maximum power output, which for systems with inhomogeneous temperature is not equivalent to the Clausius inequality. Second, we derive local Clausius and free energy inequalities for subsystems of a composite system. These inequalities differ from the total system one by the presence of an information-related contribution and build the ground for thermodynamics of quantum information processing. Our theory is used to study an autonomous Maxwell demon.

Figure 1

(a) Scheme of the autonomous quantum Maxwell demon described in the text. (b) Schematic representation of the spin exchange induced by the $XY$ interaction.

Figure 2

Steady-state work, free energy, heat, information flow, and energy flow for (a) the second and (b) the first quantum dot. Results for $T=100$, ${\epsilon }_i=0$, $U_i\to \infty$ (strong Coulomb blockade), ${\mu }_{L_1}=-{\mu }_{R_1}=60$, ${\mu }_{L_2}=-{\mu }_{R_2}=-30$, ${\mathrm{\Gamma }}_{L_1}^{\downarrow }={\mathrm{\Gamma }}_{R_1}^{\uparrow }={\mathrm{\Gamma }}_{L_1}^{\uparrow }={\mathrm{\Gamma }}_{R_2}^{\downarrow }=0$, and all other coupling strengths ${\mathrm{\Gamma }}_{{\alpha }_i}^{\sigma }$ equal to $\mathrm{\Gamma }=1$.