Landauer’s principle in the quantum regime

We demonstrate the validity of Landauer’s erasure principle in the strong coupling quantum regime by treating the system-reservoir interaction in a thermodynamic way. We show that the initial coupling to the reservoir modifies both the energy and the entropy of the system, and provide explicit expressions for the latter for a damped quantum harmonic oscillator. These contributions are related to the Hamiltonian of mean force and dominate in the strong damping limit. They need therefore to be fully taken into account in any low temperature thermodynamic analysis of quantum systems.

Figure 1

Temperature dependence of the quantities ${\Delta }^{(M)}=Q^{(M)}-kT\Delta S^{(M)}$ (blue solid line) for the mass variation alone and $\Delta =Q-kT\Delta S$ (red dashed line) for the combined transformation mass variation plus initial coupling. The former is positive, indicating an apparent violation of the Clausius inequality, while there is no violation for the combined transformation. The inset shows a comparison between the exact $\Delta$ (red dashed line) and its low temperature approximation [Eq. (13)] (red solid line). Parameters are $\omega =1.2$, $M_0=1.1$, $M_1=1.11$, $\eta =40\omega$, ${\omega }_D=1000\eta$, and $\hslash =k=1$.

Figure 2

Entropy and heat during the initial quasistatic coupling to the reservoir, $\Delta S^{(C)}$ (red dotted line) and $Q^{(C)}$ (lower red solid line), and during a quasistatic mass variation, $\Delta S^{(M)}$ (blue dashed line) and $Q^{(M)}$ (upper blue solid line), as a function of temperature. Changes for the initial coupling have opposite signs and much larger amplitudes than those for the mass variation. Parameters are the same as in Fig. 1.