The price of cooling by watching
Does a fridge that works by watching qubits feel either of its two tipping points in its energy bill?
Known, reproduced
A fridge for qubits that works by watching. Run a chain of qubits through random gates. Check each recently disturbed qubit with odds p; if it reads 1, flip it to 0. Check often enough and the whole chain freezes cold and stays cold.
The controller only needs a flag per qubit: "maybe hot" or "known cold". The flags never depend on what the checks read. So the cooling switch-off is a classical spreading process, directed percolation, the same maths as a fire that either spreads or burns out.
The controller's flags
starting
top left · time runs down; each row is one step. A gate on a pair marks both qubits "maybe hot" if either was. Then each qubit is checked with odds p and becomes "known cold" · top right · fraction still maybe-hot, log-log, against the directed-percolation slope (−0.160) · bottom · cooling power p·ρ/2 from the real 20,000-site run (moss), the slider's p (slate) and this demo's own running estimate (ember). Above p = 0.356 the flags die out and the fridge has nothing left to cool.
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In plain words
Each reading pulls out exactly half a quantum of energy on average, because the gate just before it leaves the qubit at even odds. So the cooling power is p·ρ/2, where ρ is the fraction of flags that are maybe hot. It peaks near p = 0.29: check more often than that and there are fewer hot qubits left to catch.
At p = 0.356 the flags die out for good. The fitted exponent β = 0.271 sits on directed percolation's 0.2765. That transition is classical.
The quantum transition (the measurement-induced change in entanglement) happens at a different p. The energy bill cannot see it. Even a watcher who knows everything about a single qubit's history finds the record compressible by at most 9%, with no kink at the quantum transition. Hypothesis H2, that a smarter fridge would feel it, was not supported.