Landauer’s Principle in Multipartite Open Quantum System Dynamics

We investigate the link between information and thermodynamics embodied by Landauer’s principle in the open dynamics of a multipartite quantum system. Such irreversible dynamics is described in terms of a collisional model with a finite temperature reservoir. We demonstrate that Landauer’s principle holds, for such a configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system. Quite remarkably, such a principle for heat and entropy power can be explicitly linked to the rate of creation of correlations among the elements of the multipartite system and, in turn, the non-Markovian nature of their reduced evolution. Such features are illustrated in two exemplary cases.

Figure 1

(a) Sketch of the recycled environment setup: After colliding with ${\mathcal{S}}_A$, subenvironment ${\mathcal{R}}_n$ (prepared in ${\eta }_n^{\mathrm{th}}$) is used to erase the state of ${\mathcal{S}}_B$. By tracing out the subenvironments, a Markovian ME is achieved for $\mathcal{S}$. (b) Heat flux and entropy for a system composed of two qubits erased by independent baths (no cascade) for $\xi =0.9$ and $\xi =-0.9$ (inset). (c) Heat and entropy flux for the cascade model. We have set $\gamma /\omega =1$ with $\mathcal{S}$ initially prepared in $|\uparrow \uparrow ⟩$ at $\xi =0.9$ and $\xi =-0.9$ (inset). (d) Mutual information $I(A:B)$ between the subsystems in the same case of panels (b) and (c) for $\xi =0.9$ (solid brown line) and $\xi =-0.9$ (dashed green line). Heat fluxes are expressed in unit of $\omega \gamma$.

Figure 2

(a) Sketch of the indirect-erasure protocol: The bipartite system $\mathcal{S}$ consists of subsystems ${\mathcal{S}}_A$ and ${\mathcal{S}}_B$. After ${\mathcal{S}}_B$ interacts with the $n$th subenvironment (prepared in ${\eta }_n^{\mathrm{th}}$), it collides with ${\mathcal{S}}_A$ and is then directed to element ${\mathcal{R}}_{n+1}$. ${\mathcal{S}}_B$ thus bridges the erasure process undergone by ${\mathcal{S}}_A$, which experiences a non-Markovian evolution. (b)–(e): Total heat flow $\beta \dot{Q}$ against the entropy change rate $\dot{\tilde{S}}$ for qubit-qubit [(b),(c)] and qubit-harmonic oscillator [(d),(e)] configurations. We have set $J/\omega =0.1$ and ${\gamma }_g/\omega =0.01$, taking ${\mathcal{S}}_B$ at the same temperature of the environment, $\beta =10$ [(b),(d)] and $\beta =0.5$ [(c),(e)]. A study against the value of $J$ and ${\gamma }_g$ is reported in Ref. [22].

Figure 3

We plot $\beta {\dot{Q}}_A(t)$ and ${\dot{\tilde{S}}}_A$ for the qubit-oscillator configuration in the indirect-erasure case. In panel (a) [(b)] we have used $\beta =10$ ($\beta =0.5$) and the parameters stated in Figs. 2 and 2.