Improving the efficiency of finite-time memory erasure with potential barrier shaping

TL;DR

This paper tackles the problem of finite-time memory erasure and the associated thermodynamic costs by analyzing barrier shaping in an asymmetric bistable potential. It models a Brownian particle in an overdamped Langevin framework with barrier-lowering and tilting protocols to drive erasure, and it evaluates erasure success rate, work, and heat, framing the energetics with the Landauer bound $k_B T \ln 2$ and the detailed Jarzynski equality. The main finding is that increasing asymmetry lowers the required driving amplitude and can reduce average work and heat below the Landauer limit for finite-time cycles, with an effective free-energy change $\Delta F_{eff}$ computed from $A_{01}$ and $A_{11}$ that is below the bound in asymmetric cases. These results provide a principled route to design more energy-efficient erasure protocols and have potential implications for improving the thermodynamic performance of digital devices.

Abstract

Erasure of the binary memory, 0 or 1, is an essential step for digital computation as it involves irreversible logic operations. In the classical case, the erasure of a bit of memory is accompanied by the evolution of a minimum amount of heat set by the Landauer bound kTln2, which can be achieved in the asymptotic limit. However, the erasure of memory needs to be completed within a finite time for practical and effective computational processes. It is observed that the higher the speed of erasure, the greater the amount of heat released, which leads to unfavorable environmental conditions. Therefore, this is a fundamental challenge to reduce the evolved heat related to finite-time memory erasure. In the present work, we address this crucial aspect in the field of information thermodynamics, where the two memory states correspond to the two wells of a bistable potential, as in the conventional cases. However, the potential is asymmetric in terms of the width of the two wells. Moreover, the two memory states are separated by a barrier that is asymmetric in structure. We examine in detail the effect of the degree of asymmetry on the success rate of the erasure process and the work done or heat released associated with it. We find that the asymmetry in the potential barrier partitioning the two memory states plays a very significant role in improving the efficiency of the erasure process, in view of the success rate and the thermodynamic costs. We retrieve the approach towards the Landauer limit in terms of the energetics involved with the erasure mechanism under the symmetric setup.

Figures (15)

• Figure 1: Potential $U(x)$ with different asymmetry parameter value $c$ for a fixed barrier height of $h=1$.
• Figure 2: The time-series of the tilting force $f(t)$ and the barrier-lowering force $g(t)$.
• Figure 3: Time evolution of the bistable potential with barrier height $h=1$during an erasure cycle with $A=0.7$, $\omega = 0.01$ and $Z = 0.5$ for the (a) symmetric case $c = 1$ and the (b) asymmetric case with $c = 0.2$. Each panel shows the potential landscape at different time points during the erasure protocol.
• Figure 4: Stochastic trajectories of 100 particles during the erasure process designed in bistable potentials with barrier height $h = 1$, diffusion constant $D = 0.1$, $\omega = 0.01$, and barrier-lowering depth $Z = 0.5$. Top row: Symmetric potential ($c = 1$), showing (a) incomplete erasure at low tilt $A = 0.2$, and (b) successful erasure at $A = 1$with equilibrium distribution of initial memory states.Middle row: Asymmetric potential ($c = 0.2$), showing (c) incomplete erasure at $A = 0.1$, and (d) successful erasure at $A = 0.3$with equilibrium distribution of initial memory states.Bottom row: Asymmetric potential ($c = 0.2$), showing (e) incomplete erasure at $A = 0.1$, and (f) successful erasure at $A = 0.3$with nonequilibrium distribution $(50:50)$ of initial memory states.For the cases with initial equilibrium states, the thermalization time is $t_{0}=314$. The ramp-up and ramp-down times for the tilting force are $\tau_{1}=298$ and $\tau_{2}=16$, respectively, for all cases.
• Figure 5: The erasure performance as a function of the driving amplitude of the tilting force $A$ is illustrated. Panels (a) and (b) show how the erasure rate changes with $A$ for different asymmetry parameters $c$. In both panels, barrier height $h = 1$, noise strength $D = 0.15$, the barrier-lowering depth is $Z = 0.5$, $\omega = 0.01$, $\tau_1 = 298$, and $\tau_2 = 16$. In panel (a), the results are for the erasure mechanisms when the particles are initially positioned at $x=0$ at the start of the simulations. Then they are allowed to get thermalized with the heat bath for the duration $t_{0}=314$, whereas for the data in panel (b), the particles have an initial 50-50 distribution without thermalization. For both cases, the ramp-up and ramp-down times for the tilting force are $\tau_{1}=298$ and $\tau_{2}=16$, respectively.