Heat flows from hot to cold, a rule so reliable it is enshrined in the second law of thermodynamics. In an experiment reported in Physical Review Letters, however, researchers coaxed heat to flow the other way, from a cold system to a hotter one, while simultaneously extracting work from the machine. The device behind this apparent violation is a quantum switch, a circuit that runs its operations in a superposition of two different orders, and the trick works only because a modern Maxwell’s demon is doing the bookkeeping.
The demon is the key to why the second law survives. Physicists have known since the 19th century that a clever enough gatekeeper could, in principle, sort fast and slow molecules and push heat against its natural direction. What keeps Maxwell’s demon consistent with thermodynamics is that the demon must remember which molecules it let through, and erasing that memory costs energy. In the new experiment, by a collaboration led by Zhong-Xiao Man at Qufu Normal University, Rosario Lo Franco at the University of Palermo, and Giulio Chiribella at the University of Hong Kong, the demon’s memory is an explicit part of the machine: a control qubit whose reset each cycle is the price of the heat flowing uphill.
A superposition of orders
The experiment exploits indefinite causal order, a resource unique to quantum mechanics. In a quantum switch, a control qubit in a superposition of 0 and 1 determines whether process A runs before process B or B before A, so that the two orders coexist. In the photonic implementation, photons from a down-conversion source travel through a folded interferometer about 1.8 meters (5.9 feet) long; the photon’s polarization plays the role of the system qubit, and its path plays the role of the control. Two identical thermalization channels, each built from wave plates and beam splitters, act on the system in both orders at once.
The system starts at temperature T_S and the channels act at temperature T_E. For a system hotter than the channels, the expected outcome is cooling: heat should flow out. Instead, when the control qubit is measured in the right superposition basis, the system’s mean energy increases, meaning heat flowed from the colder channels into the hotter system. The effect appears in a window where the channel temperature is more than half the system temperature; for the reverse case, where the channels are hotter, anomalous cooling appears when the temperature ratio stays below about 1.45. In the extreme case of two systems at exactly equal temperature, the switch can drive the system to infinite effective temperature, so that heat flows between systems in perfect thermal equilibrium.
Where the work comes from
The same setup runs as a quantum Otto engine, a four-stroke heat engine cycle. In the anomalous branch, the machine absorbs heat from the cold reservoir and releases it to the hot one, the signature of a refrigerator, while simultaneously outputting net work. Classically, that combination is impossible: a refrigerator requires work input, and an engine that also refrigerates would be a perpetual motion machine.
The resolution is that the engine is powered by erasing the demon’s memory. The cycle proceeds only when the control qubit is found in one particular outcome, and each successful cycle must be followed by resetting the control, an operation that costs work proportional to the information discarded. The researchers write the erasure cost into the engine’s coefficient of performance, where it plays the role of the plug in a conventional refrigerator. Unmeasured, the anomalous flows cancel: average over both control outcomes and the heat transfer returns to its classical, second-law-abiding value.
The authors also note a further subtlety: the same anomalous heat flow can be reproduced with definite causal order, using a circuit of controlled swaps that never superposes the order of events. The effect is therefore not a unique witness of indefinite causal order. What the superposition contributes is a compact, experimentally practical route: the photonic switch realizes the demon in a single interferometer, where a definite-causal-order simulation would require more elaborate controlled operations.
A proof of principle, with caveats
The temperatures in the experiment are effective temperatures of single-photon polarization states, not the temperatures of macroscopic objects, and the heat flows are measured as changes in the average energy of the system qubit conditional on the control measurement. The thermalization channels are simulated optically, and the final result is assembled from sixteen separate experiments with quantum process tomography, with channel fidelities above 99 percent. This is a proof of principle in an optical laboratory, not a machine that will cool your coffee.
What the result establishes is that the direction of heat flow in a quantum process is not fixed by temperatures alone, and that the second law’s ledger can be balanced by explicitly accounting for the control system’s information. The demon’s memory, it turns out, is where the bill lands. The finding adds to a growing body of work connecting quantum information to thermodynamics, in which causal structure, coherence, and measurement are not side effects but resources in their own right. Future work will likely explore whether the anomalous heat flow can be turned into practical advantage in quantum thermal machines, and how the erasure cost scales as the switch grows.
Sources
1. Qing-Feng Xue, Qi Zhang, Xu-Cai Zhuang, Yun-Jie Xia, Enrico Russo, Giulio Chiribella, Rosario Lo Franco, and Zhong-Xiao Man, “Anomalous Heat Flows and Quantum Otto Engine with (In)definite Causal Order,” Physical Review Letters 137, 030404 (2026). DOI: 10.1103/sx1m-pdhz. Preprint: arXiv:2511.04028.
2. Chaitanya Gupta, “Quantum principle allows heat to flow from cold to hot,” Physics World, August 10, 2026. https://physicsworld.com/a/quantum-principle-allows-heat-to-flow-from-cold-to-hot/
3. Ingrid Fadelli, “A quantum heat engine that simultaneously provides work and refrigeration,” Phys.org, July 26, 2026. https://phys.org/news/2026-07-quantum-simultaneously-refrigeration.html
4. Interesting Engineering, “New quantum heat engine produces work and refrigeration at same time.” https://interestingengineering.com/science/unusual-quantum-effect-heat-engine
5. Quantum Zeitgeist, “Quantum Otto cycle with indefinite causal order achieves anomalous heat,” November 11, 2025. https://quantumzeitgeist.com/quantum-otto-cycle-indefinite-causal-order-achieves-anomalous-heat/