Fooling the Landauer bound with a demon biased thermal bath

TL;DR

This work addresses the Landauer bound for one-bit erasure by introducing a hysteresis in a feedback-controlled virtual double-well potential, creating a non-equilibrium steady state with an adjustable effective temperature $T_{eff}$. The authors demonstrate erasure costs that can be tuned below the bound (down to about $0.78 L_0$) or above it (up to $1.30 L_0$) depending on the hysteresis sign, interpreting the effect as an embedded Maxwell demon in the feedback loop. The key contributions include a quantitative model linking hysteresis to a demon-thermal-bath temperature, experimental verification of $T_{NESS}$ between $0.7 T_0$ and $1.55 T_0$, and a framework for defining an effective Landauer bound $L_{eff}=(T_{eff}/T_0)L_0$ that governs both quasi-static and finite-time erasures. The findings reveal how memory and feedback information can modulate thermodynamic costs in stochastic information processing, with implications for energy-efficient nanoscale computation and the study of information-thermodynamics interplay.

Abstract

The Landauer principle establishes a fundamental lower bound on the energetic cost of the erasure of a one-bit memory in thermal equilibrium. Here, we experimentally demonstrate how this bound can be effectively circumvented by introducing a hysteresis in the feedback-generated virtual potential of a micro-resonator acting as the information bit. By tuning the hysteresis, we engineer a non-equilibrium steady state with an adjustable effective temperature, enabling erasure processes that consume over 20 percents below the Landauer bound. Our results reveal that the hysteresis acts as an embedded Maxwell demon, exploiting temporal and spatial information to reduce the system's entropy and the thermodynamic transformation cost. This approach provides a versatile platform for exploring the interplay between feedback, information, and energy in stochastic systems.

Figures (4)

• Figure 1: (a) Experimental setup. The deflection $x$ of a conductive cantilever (yellow) is measured using a differential interferometer Paolino2013. The cantilever behaves as a harmonic oscillator whose equilibrium position is controlled electrostatically by the voltage difference with a facing electrode. The feedback controller (dashed box), composed of a comparator and a multiplier, generates a virtual double-well potential. In the standard configuration, the switch between voltages $\pm V_1$ occurs when $x=0$; with hysteresis, the switching threshold is shifted by $\pm h$Dago-exp. (b) Feedback-induced double-well potential for $h=0$. Experimental potential (blue) reconstructed from the measured probability distribution function (PDF) of $x$ using the Boltzmann relation, in excellent agreement with the theoretical form $U(x)=\frac{1}{2}(|x|-x_1)^2$ (dashed red). (c) Energy pumping induced by the hysteresis. For $h=0$ (bottom), the switching occurs exactly at $x=0$, so the system crosses smoothly between wells without accumulating potential energy. For $h>0$ (top), the delayed switch allows the cantilever to store additional potential energy, at the expense of losing some kinetic energy. This energy exchange occurs at every switching event biased by the "demon" hysteresis.
• Figure 2: (a) Sketch of the erasure to $0$ protocol. The two wells are first merged in a time $\tau$, the resulting single well is translated to the left in the same time $\tau$, and finally the initial double well is restored. Any initial condition end in logical state $0$. (b) Work and heat distributions for quasi-static erasures performed with hysteresis parameters $h=0.17$ and $h=-0.10$. The protocol is the one of Eq. \ref{['Uprotocol']} with duration $\tau=1s$. The average heat (PDF in dotted lines) perfectly matches the average work (PDF in plain lines) in both cases. For $h=0.17$ (blue), 1-bit erasures -- on the cooled down system -- require on average $78\%$ of the Landauer bound (dashed blue vertical line): $\langle \mathcal{W} \rangle =0.53 \pm 0.005$ and $\langle \mathcal{Q} \rangle= 0.54 \pm 0.02$. For $h=-0.10$ (red), the average energy cost (dashed red vertical line) -- on the warmed up system -- reaches $120\%$ of the Landauer bound: $\langle \mathcal{W} \rangle= 0.89\pm 0.015$ and $\langle \mathcal{Q} \rangle =0.91 \pm 0.02$.
• Figure 3: (a) Experimental PDFs of velocity for different hysteresis parameters $h$. The velocity $\dot x$ is measured over $10s$ of free evolution in a static double-well potential with centers in $\pm x_1=\pm1$ (chosen to maximize the effect), while varying the feedback hysteresis $h$. All PDFs remain Gaussian with variances (kinetic temperature) shown in (b) (blue crosses). For $h=0$, the Boltzmann equilibrium (normal distribution with variance $1$) is recovered (dashed black line). (b) Kinetic temperature $T=\langle \dot x^2 \rangle$ versus hysteresis parameter $h$. Negative hysteresis increases the effective temperature (heating), whereas positive hysteresis decreases it (cooling), in excellent agreement with the theoretical prediction from Eq. \ref{['eqhyst']} (dashed red). (c) Temperature evolution during quasi-static erasure with feedback hysteresis $h=0.17$. The temperature, extracted from the time-dependent velocity variance averaged over $N=2000$ trajectories, decreases during the first $\tau=1s$ of the protocol due to the cooling effect of hysteresis in the virtual double-well. The amplitude of this cooling depends on the instantaneous well separation $x_1(t)$ and follows closely the theoretical model of Eq. \ref{['eqhyst']} (dashed red), as expected in the quasi-static regime.
• Figure 4: Fast erasure cost$\langle \mathcal{W} \rangle$ and $\langle \mathcal{Q} \rangle$ for erasure protocols plotted as a function of the usual $\tau_{\mathrm{relax}}/\tau$ scaling. Experimental data ($h=0.17$, blue markers) shows an asymptotic approach in $1/\tau$ (dashed red fit) to the effective Landauer bound $L_{\mathrm{eff}}= (T_{\textrm{eff}}/T_0) L_0$. The scaling of the energetic cost of fast erasures is similar to the case without hysteresis ($h=0$, grey markers and dashed line fit Dago-2022), only the asymptote differs.