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

Abstract

Erasure of the binary memory, 0 or 1, is an essential step for digital computation involving irreversible logic operations. The erasure of a bit of a classical bit of memory is accompanied by the evolution of a minimum amount of heat set by the Landauer bound kTln2, achieved in the asymptotic limit. However, the erasure of memory needs to be completed within a finite time for practical computation. The higher the speed of erasure, the greater the amount of heat released, which is unfavorable to the environment. Therefore, this is a fundamental challenge to reduce the evolved heat related to finite-time memory erasure. Here, we address this crucial aspect of information thermodynamics. We proceed by considering the model where the two memory states correspond to the two wells of a bistable potential that is asymmetric in terms of the width of its two wells. Moreover, they are separated by an asymmetric barrier. This type of asymmetry models the two binary memory states occupying different phase-space volumes, but are energetically equivalent. We examine 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 this characteristic asymmetry in the underlying potential plays a very significant role in improving the efficiency of the erasure process. Our study establishes the fact that one can reach below the Landauer bound in an appropriate asymmetric setup. Importantly, it develops a quantitative understanding of the deviation from the Landauer limit as a function of the degree of asymmetry in the governing potential. We identify the effective free energy change for the finite-time bit erasure process as a general lower bound for the work done or evolved heat even when the departure from the Landauer limit is observed. We retrieve the approach towards the Landauer limit under the symmetric setup.