The microcantilever oscillates at 1270 Hz, and its position controls a virtual potential: an invisible energy landscape with two wells, created by feedback. Normally, switching between the wells occurs when the system crosses the zero point, but now a delay comes into play: the threshold is shifted by an amount h. With positive hysteresis (h=0.17), the system switches late, and each transition draws a little energy out of the oscillator, as if an invisible demon were slowing the bit down and cooling it. As a result, the effective temperature (the temperature of a nonequilibrium system inferred from fluctuations) drops to 0.78 of the thermostat temperature, and the average work of erasing one bit turns out to be 0.53 kBT0, which is 22% below the Landauer bound, long considered an absolute limit.
This trick became possible because the switching delay stores information about the system's past. Maxwell's demon, an imaginary being that sorts molecules without expending energy, is realized here not as an external agent but as a hidden variable inside the feedback itself. Hysteresis (the delay in switching when the signal changes) acts as a built-in observer: it remembers where the system came from and uses that knowledge to extract work from thermal fluctuations. With negative hysteresis (h=-0.10), switching occurs early, adding energy, and the effective temperature rises to 1.20 T0, while the erasure work increases to 1.30 of the Landauer bound. An experiment on a microcantilever with a resonance frequency of 1270 Hz confirmed the model: the measured kinetic temperature (the temperature calculated from particle velocities) matched the predictions for the effective temperature.
Before this work, it was believed that the Landauer bound could be circumvented in a classical system only with the help of an external demon that explicitly stores information. Now it is clear: hysteresis in the feedback itself plays the role of such a demon, creating a nonequilibrium state with reduced entropy. The discovery does not violate the second law of thermodynamics; it is just that the information encoded in the delay was not accounted for in previous calculations. The practical benefit is obvious for microelectromechanical systems and logic devices, where every joule counts: a 22% reduction in heat dissipation when erasing a bit could be an important step toward energy-efficient computing.
In the future, this approach could be extended to quantum systems, where the demon might exploit entanglement, or to other physical platforms such as optical traps and nanomagnets. The question of how hysteresis relates to non-Markovian dynamics, where memory of the past plays a key role, remains open. The microcantilever oscillating in a virtual potential has become a tiny laboratory where the fundamental limit of information turned out to be movable, if only the right delay is added.
At room temperature, the Landauer bound is about 3×10⁻²¹ J, which is billions of times less than the energy a modern transistor consumes per switching event.
The idea of a demon controlling a system to circumvent thermodynamic laws is reminiscent of the plot of Stanisław Lem's short story "The Maxwell Demon," in which a being sorts molecules, violating the second law of thermodynamics.