Repeated Interactions and Quantum Stochastic Thermodynamics at Strong Coupling

The thermodynamic framework of repeated interactions is generalized to an arbitrary open quantum system in contact with a heat bath. Based on these findings, the theory is then extended to arbitrary measurements performed on the system. This constitutes a direct experimentally testable framework in strong coupling quantum thermodynamics. By construction, it provides many quantum stochastic processes and quantum causal models with a consistent thermodynamic interpretation. The setting can be further used, for instance, to rigorously investigate the interplay between non-Markovianity and nonequilibrium thermodynamics.

Figure 1

A system $S$ is in contact with a bath initialized at temperature $T$ (we do not imply that the bath must be kept at a well-defined temperature at later times). In a preparation apparatus $P$ units $U(k)$ are sequentially produced, which interact with the system when they enter the shaded gray area and which are afterward detected in $D$ giving rise to the measurement outcome $r_k$ (properly introduced later on in the text). Note that each unit can be different in principle. We also remark that the description of the units does not need to be taken literally in the sense that they are merely “ancillas” required for a consistent thermodynamic description of a non-Markovian quantum stochastic process, as introduced later on.