Impossibility of Refrigeration and Engine Operation in Minimal Qubit Repeated-Interaction Models

• URL: http://arxiv.org/abs/2602.18300v1
• Date: Fri, 20 Feb 2026 15:53:52 GMT
• Title: Impossibility of Refrigeration and Engine Operation in Minimal Qubit Repeated-Interaction Models
• Authors: Gabrielle Barsky-Giles, Alessandro Prositto, Matthew Gerry, Dvira Segal,
• Abstract summary: We investigate the operation of a qubit as a quantum thermal device within the repeated interaction framework.<n>We analyze two minimal models: an alternating-coupling setup, and a simultaneous-coupling setup.<n>Our results establish fundamental limitations on qubit-based quantum thermal machines operating under Markovian repeated interactions.
• Score: 39.146761527401424
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the operation of a qubit as a quantum thermal device within the repeated interaction framework, allowing for strong system-bath coupling and finite interaction times. We analyze two minimal models: an alternating-coupling setup, in which the qubit sequentially interacts with hot and cold baths, and a simultaneous-coupling setup, where both baths interact with the qubit during each collision. For the alternating model, we obtain an exact analytical solution for the limit-cycle state, valid for arbitrary coupling strengths and collision durations. Using this solution, we rigorously prove a no-go theorem for quantum refrigeration. We further demonstrate that, although work can be generated locally at individual system-bath contacts, the total work over a cycle is always nonpositive, precluding engine operation. In the absence of work, the model describes pure heat conduction, for which we derive a closed-form expression for the heat current and show that it exhibits a nonmonotonic turnover behavior. The simultaneous-coupling model is analyzed perturbatively. In the short-collision-time limit, it reproduces the same steady-state behavior as the alternating model, reinforcing the generality of the constraints identified. Our results establish fundamental limitations on qubit-based quantum thermal machines operating under Markovian repeated interactions and highlight the need for enriched models to realize functional quantum thermal devices.

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