Catégorie : preprint

Nicolas Barros, Stephen Whitelam, Sergio Ciliberto, Ludovic Bellon, submitted to J. Stat. Mech.

arXiv: 2609.11473

We use evolutionary reinforcement learning to determine efficient time-dependent erasure protocols for an underdamped cantilever moving in a double-well potential, an experimental realization of a 1-bit memory. We investigate how the mean work ⟨W⟩ needed to erase a bit scales as a function of the protocol duration τ. We find two regimes, depending on how τ compares to the relaxation time of the system t_r. For τ≫t_r, the quasistatic isothermal regime, we recover Landauer’s bound plus an overhead that scales as 1/τ, similar to the overdamped case. By contrast, for τ<t_r erasure becomes adiabatic and ⟨W⟩ grows more slowly than in the isothermal case. This growth is bounded from below as 1/τ, which we derive using a gedanken optimal protocol. Finally, comparison with overdamped erasure shows that learned protocols can outperform protocols that are optimal subject to equilibrium boundary conditions.

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Natalia Ruiz-Pino, Ludovic Bellon, Antonio Prados, submitted to Phys. Rev. X

arXiv: 2607.27299

Information engines exploit feedback to extract work from thermal fluctuations, extending the second law of thermodynamics through information-theoretic bounds. While several such bounds have been proposed, their relative performance under realistic conditions — where measurements are noisy and feedback is temporally correlated — remains largely unclear. Here, we experimentally and theoretically investigate this problem in an underdamped feedback-controlled system with Markovian measurements but non-Markovian control sequences. We compare three representative bounds derived from transfer entropy, unavailable information, and Markovian mutual information, and find that none is universally optimal. Instead, measurement noise preferentially affects information measures that rely on detailed trajectory statistics, while leaving quantities based on instantaneous correlations comparatively robust. As a consequence, trajectory-dependent bounds deteriorate rapidly, giving rise to a crossover in which the Markovian mutual-information bound becomes tighter than the unavailable-information bound over a broad range of measurement noise. Our results reveal a general limitation of information-theoretic descriptions that rely on detailed trajectory statistics in realistic settings and provide a unified perspective on information thermodynamics beyond idealised feedback protocols.

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Stephen Whitelam, Sergio Ciliberto, Ludovic Bellon, submitted to Phys. Rev. E

arXiv: 2607.06822

We train a neural-network Maxwell’s demon to extract work from a model of an underdamped micromechanical cantilever subject to thermal noise. The demon, which periodically adjusts the position of a harmonic trap, is trained to maximize the power extracted under steady-state operation. When the demon is given the cantilever position and trap position as inputs it learns a refined version of an existing hand-designed protocol, yielding a substantial improvement in performance. When the demon receives the oscillator velocity as input it discovers a qualitatively different strategy that extracts substantially more work, close to the theoretical power bound. Analysis of the protocol shows that it implements cold damping: the trap position is displaced approximately linearly with velocity, producing an effective increase of the oscillator’s damping coefficient and a reduction of its effective temperature. Thus a neural-network Maxwell’s demon rediscovers a well-known cooling strategy from optomechanics, revealing a simple physical mechanism underlying near-optimal work extraction from thermal fluctuations in an underdamped system.

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Aubin Archambault, Caroline Crauste-Thibierge, Alberto Imparato, Sergio Ciliberto, Ludovic Bellon, submitted to Phys. Rev. E

arXiv: 2607.01405

We derive the distribution of the first passage time t_fp for the position x of an underdamped harmonic oscillator to overcome a threshold x_B. As the tfp distribution depends on the oscillator quality factor Q different approaches are used. At very large quality factor (Q≫100) and intermediate and long tfp the proof is based on an energy diffusion model, whereas at medium quality factor (Q∼10) the proof is based on the study of the eigenvalues of the Kramers linear differential operator with absorbing boundary conditions. For all Q and short t_fp we use a Hamiltonian approximation. The theoretical predictions are in excellent agreement with direct numerical simulations of underdamped oscillator dynamics. Finally we show that the mean of the trajectories ending at t_fp presents a particular shape driven by a specific noise pattern.

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Aubin Archambault, Caroline Crauste-Thibierge, Alberto Imparato, Sergio Ciliberto, Ludovic Bellon, submitted to Phys. Rev. Lett.

arXiv: 2607.01405

The distribution of the first passage time t_fp for the position x to overcome a threshold x_B is calculated in an underdamped harmonic oscillator. The proof combines several approaches based on the determination of the eigenvalues of the Kramers differential operator for the intermediate and long time regimes and on a Hamiltonian approximation for the short times. The theoretical predictions are in excellent agreement with the results of an experiment on an underdamped micro-cantilever. The knowledge of the t_fp distribution opens the way to several applications, among them the precise estimation of the power of information engines, which we have also experimentally checked.

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