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

TL;DR

This paper proves fundamental limitations on qubit-based quantum thermal machines within repeated interaction models, showing no possibility for refrigeration or engine operation under these conditions, and analyzing heat conduction behavior.

Contribution

It provides an exact analytical solution for the alternating model's limit-cycle state and establishes a no-go theorem for quantum refrigeration in minimal qubit models.

Findings

No-go theorem for quantum refrigeration in minimal models

Total work over a cycle is always nonpositive, precluding engine operation

Heat current exhibits nonmonotonic turnover behavior

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.