The work sits at the intersection of stochastic thermodynamics and information physics, alongside research on Maxwell's demon and the Landauer principle. Elsewhere it has already been shown how quantum sensors beat noise and how quantum computers repair themselves, as well as how a demon prefers indistinguishable photons. This paper follows the general quest to circumvent thermodynamic constraints through feedback, but stands out by being the first to experimentally demonstrate a reduction in the cost of erasing a bit below the Landauer bound using hysteresis in a classical system.
The experiment was performed on a microcantilever with a resonance frequency of 1270 Hz, placed in a virtual double-well potential created by feedback. The feedback is controlled by a comparator with adjustable hysteresis: switching between wells occurs when the threshold ±h is reached instead of zero. For positive hysteresis (h=0.17), the system switches with a delay, which leads to energy being extracted from the oscillator at each transition. For negative hysteresis (h=-0.10), switching occurs ahead of time, adding energy. The system temperature is measured from the velocity variance, and work and heat are computed from stochastic trajectories. The erasure protocol takes 1 second, which is much longer than the relaxation time of 2.5 ms, ensuring a quasistatic regime.
At h=0.17, the average erasure work was 0.53±0.005 in units of kBT0, which equals 0.78 of the Landauer bound L0 = ln 2. The average heat was 0.54±0.02, which within error coincides with the work. At h=-0.10, the average work rose to 0.89±0.015, that is, 1.30 of L0. The model predicts an effective temperature Teff = 0.78 T0 for positive hysteresis and Teff = 1.20 T0 for negative hysteresis, which agrees with measurements of the kinetic temperature. For fast erasures with finite time τ, the usual 1/τ dependence is observed, but the asymptote converges to an effective Landauer bound rather than the standard one.
Unlike neighboring works where cost reduction was achieved through quantum effects or special initial states, here a purely classical method is used: hysteresis in feedback. This is the first experimental demonstration that a built-in Maxwell's demon can be realized in a classical system and lead to an apparent violation of the Landauer principle. The work shows that the information stored in the switching delay is a hidden variable that reduces the system's effective entropy.
The topic could develop toward optimizing erasure protocols with hysteresis in mind to minimize energy consumption in real devices. A generalization to quantum systems, where the demon could exploit quantum entanglement, is possible. It would also be interesting to explore the connection between hysteresis and non-Markovian dynamics, where the hidden variable plays the role of memory.
The results could influence the design of energy-efficient logic elements and stochastic engines, where feedback is already used for control.
The next step could be an experimental test of erasure with hysteresis in other physical systems, for example, in optical traps or nanomagnets, to confirm the universality of the effect.
The work is directly related to the problem of defining the cost of information under nonequilibrium conditions and to the paradox of Maxwell's demon. It shows how hidden variables in feedback can alter the effective temperature and, consequently, the thermodynamic limits of computation.
At room temperature, the Landauer bound is about 3×10⁻²¹ J, which is billions of times less than the energy consumed by a modern transistor per switching event.
The idea of a demon controlling a system to circumvent thermodynamic laws recalls the plot of Stanisław Lem's short story 'The Maxwell Demon,' in which a being sorts molecules, violating the second law of thermodynamics.